Texas Instruments TI-80 Скачать руководство пользователя страница 31

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Operating the TI-80 1-5

In most cases, the appearance of the cursor indicates what
will happen when you press the next key.

Cursor

Appearance

Meaning

Entry

Blinking

The next keystroke is
entered at the cursor; it
types over any character.

INS

(insert)

Blinking

The next keystroke is
inserted at the cursor.

2nd

Blinking

The next keystroke is a

2nd

operation.

ALPHA

Blinking

The next keystroke is an
alphabetic character.

memory

“full”

Checkerboard
rectangle

You have entered the
maximum number of
characters in a name, or
memory is full.

Graphs and the screens for viewing and editing tables and lists
have different cursors, which are described in the appropriate
chapters.

When the TI

80 is calculating or graphing, a vertical line

shows in the upper right of the display as a busy indicator.
During a pause in a program, the busy indicator is a dotted
line.

Display Cursors

Busy Indicator

Содержание TI-80

Страница 1: ...K TI GRAPH LINK Calculator Based Laboratory CBL CBL 2 Calculator Based Ranger CBR Constant Memory Automatic Power Down APD and EOS are trademarks of Texas Instruments Incorporated Windows is a registe...

Страница 2: ...suant to Part 15 of the FCC rules These limits are designed to provide reasonable protection against harmful interference in a residential installation This equipment generates uses and can radiate ra...

Страница 3: ...alculation 6 Defining a Function Box with Lid 7 Defining a Table of Values 8 Zooming In on the Table 9 Changing the Viewing Window 11 Displaying and Tracing the Graph 12 Zooming In on the Graph 13 Oth...

Страница 4: ...g Started Graphing a Circle 4 2 Defining a Graph 4 3 Setting Graph Modes 4 4 Defining Functions in the Y List 4 5 Evaluating Y Functions in Expressions 4 7 Selecting Functions 4 8 Defining the Viewing...

Страница 5: ...Getting Started Generating a Sequence 8 2 About Lists 8 3 LIST OPS Operations 8 6 LIST MATH Operations 8 9 Getting Started Building Height and City Size 9 2 Setting Up a Statistical Analysis 9 8 The...

Страница 6: ...Circle and Trigonometric Curves 11 3 Program Newton s Numerical Solve Routine 11 4 Program Numerical Integration 11 6 Program Window Variables Store and Recall 11 8 Graphing the Inverse of a Function...

Страница 7: ...nu Map A 20 TI 80 Variables A 26 Battery Information B 2 Accuracy Information B 8 In Case of Difficulty B 10 Service and Support Information B 14 Warranty Information B 15 Appendix A Tables and Refere...

Страница 8: ...porate features from different functional areas of the calculator These examples can help you see how different functional areas work together to accomplish meaningful tasks Chapter 12 describes memor...

Страница 9: ...debook each step is numbered in the order in which it is performed No other text in the guidebook is numbered therefore when you see numbered text you know you should perform the steps sequentially Li...

Страница 10: ...ining important terms used throughout the guidebook An alphabetical table of functions and instructions in Appendix A showing their correct formats how to access them and page references for more info...

Страница 11: ...have arguments returns a value and can be used in an expression A function is also the expression entered in the Y editor used in graphing The Home screen is the primary screen of the TI 80 where exp...

Страница 12: ...8 pixels high On the TI 80 real numbers are individual decimal or fraction values A value is a single decimal or fraction number or a list of decimals or fractions A variable is the name given to a lo...

Страница 13: ...the TI 80 more quickly by completing both of these examples first TI 80 Keyboard 2 First Steps 3 TI 80 Menus 4 Entering a Calculation Compound Interest 5 Continuing a Calculation 6 Defining a Functio...

Страница 14: ...ific Calculator These keys are most frequently used to access the interactive graphing features of the TI 80 These keys are most frequently used for editing expressions and values These keys are most...

Страница 15: ...ess and release 2 and then press and hold 8 to make the display lighter or press and hold 7 to make the display darker You can press M to clear the display E x 2 Press and release 2 and then press Pre...

Страница 16: ...s highlighted and the items in that menu are displayed Use 9 or 6 to display a different menu Selecting an Item from a Menu The number of the current item is highlighted If there are more than seven i...

Страница 17: ...For the first guess compute the amount available at the end of 10 years Enter the expression just as you would write it Use 1000 for the amount Press 1000 p 1 06 Z 10 2 Press to evaluate the expressi...

Страница 18: ...ed at the end of the expression 2 You can edit the expression Press 6 to move the cursor over the 2 Then type 1 9 to change 12 to 11 9 Press to evaluate the expression Note This process can be continu...

Страница 19: ...2X A W 2X 2B L V A B X Substituting V W 2X L 2 X X W X X A B X B L If necessary press z to change the MODE to FLOAT Then press y to return to the Home screen and clear it 1 Press 8 5 W to store the wi...

Страница 20: ...accept TBLMIN 0 3 Press 5 to define the table increment TBL 5 4 Press y above s to display the table Note that the maximum value is around 1 5 between 1 and 2 5 Press and hold to scroll the table unt...

Страница 21: ...alue of TBL you can zoom in on the table 1 Adjust the table setup to get a more accurate estimate of the maximum size of the cutout Press 1 to set TBLMIN Press 1 to set Tbl 2 Press y 3 Use and to scro...

Страница 22: ...1 59 6 Press or to move the cursor to 1 58 Press to move the cursor into the Y1 column The bottom line of the display shows the value of Y1 at 1 58 in full precision 33 073824 7 Press to display the...

Страница 23: ...indow variables here The standard Window variables define the viewing window as shown XMIN XMAX YMIN and YMAX define the boundaries of the display XSCL and YSCL define the distance between tick marks...

Страница 24: ...e X and Y coordinate values for the position of the graph cursor 3 Use and to position the free moving cursor at the apparent maximum of the function As you move the cursor X and Y coordinate values a...

Страница 25: ...the left of the item or you may press until the item number is highlighted and then press 2 To ZOOM IN press 2 The graph is displayed again The cursor has changed to indicate that you are using a Zoo...

Страница 26: ...to four functions Chapter 4 and up to three parametric functions Chapter 5 You can use Draw operations to annotate graphs Chapter 7 You can create function evaluation tables to analyze multiple functi...

Страница 27: ...rast 1 3 The Display 1 4 Entering Expressions and Instructions 1 6 The Edit Keys 1 8 Setting Modes 1 9 TI 80 Modes 1 10 Variable Names 1 12 Storing and Recalling Variable Values 1 13 Last Entry 1 14 L...

Страница 28: ...To prolong the life of the batteries APD turns the TI 80 off automatically after several minutes without any activity When you press the calculator shows the same screen or editor in which you left i...

Страница 29: ...ken the screen press and hold 7 To decrease the contrast lighten the screen press and hold 8 Note The display may become completely blank if you adjust the contrast setting too low If this happens pre...

Страница 30: ...t line On numeric editors such as the Window screen Chapter 4 an expression scrolls to the left and right When an entry is executed on the Home screen the answer is displayed on the right side of the...

Страница 31: ...a 2nd operation ALPHA Blinking The next keystroke is an alphabetic character memory full Checkerboard rectangle You have entered the maximum number of characters in a name or memory is full Graphs an...

Страница 32: ...n is completed when you press regardless of the cursor location The entire expression is evaluated according to Equation Operating System EOSTM rules and then the answer is displayed Note EOS rules de...

Страница 33: ...e and LOG are functions Some functions take more than one argument which is indicated by a at the end of the name MIN requires two arguments in this example MIN 5 8 An instruction initiates an action...

Страница 34: ...ssion Evaluates an expression or executes an instruction M On a line with text on the Home screen clears blanks the current line On a blank line on the Home screen clears everything on the Home screen...

Страница 35: ...ints SEQUENTIAL SIMUL Whether to plot simultaneously To change the mode setting 1 Press 8 or 7 to move the cursor to the line of the setting that you want to change The setting that the cursor is on b...

Страница 36: ...4567 4 Note If you select normal display format but the answer cannot be displayed in 10 digits or the absolute value is less than 001 the TI 80 displays the answer in scientific notation Decimal sett...

Страница 37: ...them for example the result of 2 6 2 6 is displayed as 2 3 MANSIMP displays fraction results without automatic simplification for example the result of 2 6 2 6 is displayed as 4 6 FUNC function graphi...

Страница 38: ...de Statistical plots PLOT1 PLOT2 PLOT3 on the STAT PLOTS menu System variables XMIN XMAX and others on various menus Programs have user defined names also and share memory with variables Program names...

Страница 39: ...ress If you entered an expression it is evaluated The value is stored in the variable To display the value of a variable enter the variable name on a blank line on the Home screen and then press You c...

Страница 40: ...es the Last Entry storage area only when you press you can recall the previous entry even if you have begun entering the next expression However when you recall Last Entry it replaces what you have ty...

Страница 41: ...evious entry contained more than one expression or instruction separated with a colon page 1 6 they all are recalled You can recall all entries on a line edit any of them and then execute all of them...

Страница 42: ...lot that is 1 7 meters by 4 2 meters Then calculate the yield per square meter if the plot produces a total of 147 tomatoes 1 7 p 4 2 147 e y You can use the value in ANS as the first entry in the nex...

Страница 43: ...of the current item is highlighted If there are more than seven items on the menu a appears on the last line in place of the colon between the menu number and name Menu items such as VARS WINDOW that...

Страница 44: ...ng a selection from the menu To return to the Home screen press 2 To return to the screen where you were press M To display a different menu press the appropriate key such as To select another screen...

Страница 45: ...3 TABLE TBLMIN and TBL variables 4 SIMPFACTOR Factor last used by SIMP function The Y VARS menus display the names of functions and the instructions to select or deselect functions from a program or...

Страница 46: ...where the second argument is a multi argument function or a single argument function that precedes the argument such as 2NDERIV A A 6 or ASIN 2 6 Permutations nPr and combinations nCr 7 Multiplication...

Страница 47: ...entheses are also used to enclose the arguments for certain functions for example NDERIV A A 6 In these cases parentheses do not indicate implied multiplication To enter a negative number use the nega...

Страница 48: ...If you select GOTO the cursor is displayed at the location where the error was detected Note If a syntax error was detected in the contents of a Y function during program execution GOTO returns the us...

Страница 49: ...re accessed from the keyboard others are accessed through menus Getting Started Lottery Chances 2 2 Using the TI 80 Functions 2 3 Keyboard Math Operations 2 4 MATH MATH Operations 2 7 MATH NUM Number...

Страница 50: ...ATH PRB menu Press 3 to select nCr Press 6 to enter the number of items selected 2 Press to evaluate the expression This is the total number of possible combinations of 6 numbers drawn from a set of 5...

Страница 51: ...by element basis If two lists are used in the same expression they must be the same length For more information about lists see Chapter 8 Some math functions x b c a b c DEC accept fractions as input...

Страница 52: ...nterpreted according to the current RADIAN DEGREE mode setting Refer to page 1 9 for instructions on changing the mode setting For example SIN 30 in RADIAN mode returns L 9880316241 in DEGREE mode it...

Страница 53: ...value Note Raising a negative number to a noninteger power can result in a complex number which returns an error These functions find the logarithm l power of ten 2 h and natural log x of the specifie...

Страница 54: ...For example LA2 returns a negative number because squaring is evaluated before negation Use parentheses to square a negated number LA 2 ABS absolute value 2 P returns the absolute value of a number e...

Страница 55: ...m a program INT integer divide MATH MATH item 1 returns the quotient or quotient and remainder resulting from the division of two integers Each argument can be a list integerAINT integerB When INT is...

Страница 56: ...d of an expression value can be a list value8DEC expression8DEC 3 cube MATH MATH item 3 returns the cube of a number expression or list value3 3 cube root MATH MATH item 4 returns the cube root of a n...

Страница 57: ...1 3 is used NDERIV expression variable value or NDERIV expression variable value H NDERIV uses the symmetric difference quotient method as shown in the formula below which approximates the numerical...

Страница 58: ...ls 9 If the number of decimals is omitted the number is rounded to the digits that are displayed a maximum of 10 digits Round value decimals Round value ZPART integer part MATH NUM item 2 returns the...

Страница 59: ...of the larger of each pair of elements If a list and a value are compared it compares each element in the list to the value MIN valueA valueB MAX valueA valueB MIN list MAX list MIN listA listB MAX l...

Страница 60: ...al 5 RANDINT Random integer generator RAND random number MATH PRB item 1 generates and returns a random number greater than 0 and less than 1 as in the first example below A random number is generated...

Страница 61: ...tems and number must be nonnegative integers Both items and number can be lists items nPr number items nCr number factorial MATH PRB item 4 returns the factorial of a positive integer or list of integ...

Страница 62: ...5 P8Rx Returns x given R and q 6 P8Ry Returns y given R and q degree ANGLE item 1 lets you designate an angle or list of angles as degrees regardless of the current angle mode setting In RADIAN mode c...

Страница 63: ...gular coordinates to polar coordinates and returns r R8Pq ANGLE item 4 converts the given rectangular coordinates to polar coordinates and returns q Both X and Y can be lists R8Pr X Y R8Pq X Y RADIAN...

Страница 64: ...and valueB can be numbers expressions or lists Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values valueA va...

Страница 65: ...ted 02 15 01 9 53 AM Page 1 of 10 This chapter describes how to use the fraction operations on the TI 80 Getting Started Working with Fractions 3 2 Setting Modes for Fraction Results 3 4 Entering and...

Страница 66: ...MANSIMP mode is selected the SIMP function from the FRACTION menu can be used to simplify fractions step by step 1 Select MANSIMP mode 2 From the Home screen press 1 2 6 2 _ 27 1 2 1 2 _ 9 to enter t...

Страница 67: ...on 6 Press M to clear the screen Reenter the expression or press 2 until you see the expression 1 6 27 1 1 9 7 Press 2 6 2 c 2 9 b 9 d This adds the simplification factor 9 and places the expression i...

Страница 68: ...es place before the expression is evaluated Then the result is simplified to its lowest terms For example 12 16 is simplified to 3 4 when you press There are two formats for displaying fractions resul...

Страница 69: ...the fraction You can then use b c or a b c to change the display format of the fraction result Typically you use the MANSIMP simplification mode with the a b c display format mode for teaching or lea...

Страница 70: ...s and then press 2 _ 2 Enter the denominator up to and including 1000 For example press 2 2 _ 3 to enter 2 3 A mixed fraction is fraction that has both a whole number and a fractional part for example...

Страница 71: ...ion result is 1000 or if the results of operations with these functions are not within the limits shown on page 3 6 the results are given in decimal form Other functions accept fraction entries but co...

Страница 72: ...Converts a decimal to a fraction based on mode 5 8DEC Converts a fraction to a decimal SIMP simplify fraction FRACTION item 1 simplifies the specified fraction and displays it along with the simplifi...

Страница 73: ...c convert to simple fraction FRACTION item 2 converts value to a simple fraction 8a b c convert to mixed fraction item 3 converts value to a mixed fraction value8b c value8a b c Both 8b c and 8a b c...

Страница 74: ...d or if the denominator of the equivalent fraction is greater than 1000 the decimal equivalent is returned The form of the 8FRAC result depends on the current fraction display format For example 1 25...

Страница 75: ...Circle 4 2 Defining a Graph 4 3 Setting Graph Modes 4 4 Defining Functions in the Y List 4 5 Evaluating Y Functions in Expressions 4 7 Selecting Functions 4 8 Defining the Viewing Window 4 9 Displayin...

Страница 76: ...tom half of the circle is defined by Y2 100 X2 However you can also define one function in terms of another so to define Y2 LY1 press 2 G to display the Y variables menu 1 to select Y1 2 Press 6 to se...

Страница 77: ...res are described in detail on the following pages 1 Set the mode to FUNC graphing Chapter 1 2 Enter or edit a function in the Y list page 4 5 3 Select the Y function you want to graph page 4 8 4 Defi...

Страница 78: ...er Differences in parametric graphing are described in Chapter 5 The mode settings can affect how functions are graphed RADIAN or DEGREE mode may affect how some functions are interpreted CONNECTED or...

Страница 79: ...evaluates to a value that is not a real number that point is not plotted an error does not occur The independent variable in the function is X You may press rather than pressing X to enter the X vari...

Страница 80: ...ome screen or from a program begin on a blank line 1 Press enter the expression and then press again 2 Press 3 Press 2 G and then select the name of the function from the Y menu The name is copied to...

Страница 81: ...2 G 1 c 2 G 2 c d d To evaluate the functions first specify the value of X Note that X may be a list 2 M 2 G 2 c 3 d 2 G 1 c 2 G 2 c 3 d d 2 G 3 c 2 1 2 3 2 d You can also evaluate functions without u...

Страница 82: ...ow deselected If it was deselected it is now selected Note When you enter or edit a function it is selected automatically When you clear a function it is deselected To select functions from the Home s...

Страница 83: ...dow variable value 1 Press 8 to move to the Window variable you want to change 2 To enter a real value which can be an expression you may do any of the following Position the cursor and then make the...

Страница 84: ...on 6 Press to complete the instruction Note You can use a Window variable in an expression by performing steps 3 4 and 5 The variables X and Y define the distance between the centers of two adjoining...

Страница 85: ...tely if nothing has changed that requires the functions to be replotted since the last time the graph was displayed If you have changed any of the following since the graph was last displayed pressing...

Страница 86: ...aph without the cursor or coordinate values press or M When you press 6 9 7 or 8 the cursor begins to move from the same position The free moving cursor moves from dot to dot on the screen When you mo...

Страница 87: ...calculated from the X value that is Y Yn X If the function is undefined at an X value the Y value is blank Trace cursor on the curve If the Y value of a function is above or below the viewing window...

Страница 88: ...r Press or M to see the graph without the Trace cursor Press 2 to return to the Home screen The Trace cursor remains in the same location if you leave TRACE and return as long as Smart Graph has not c...

Страница 89: ...of a box to define a new viewing window 1 Select ZBOX from the ZOOM menu The different cursor at the center of the screen indicates that you are using a Zoom instruction 2 Move the cursor to any corne...

Страница 90: ...s the viewing window by XFACT and YFACT updates the Window variables and replots the selected functions centered on the cursor location 3 ZOOM IN is still turned on To zoom in on the graph again At th...

Страница 91: ...kes the graph of a circle look like a circle XSCL and YSCL remain unchanged The midpoint of the current graph not the intersection of the axes becomes the midpoint of the new graph ZSTANDARD replots t...

Страница 92: ...then press 1 to select WINDOW 2 Press 9 to select XFACT or 0 to select YFACT XFACT or YFACT is copied to the cursor location 3 Press The Zoom factor is displayed To set the Zoom factors XFACT and YFAC...

Страница 93: ...quations on the TI 80 Before doing parametric graphing you should be familiar with Chapter 4 Function Graphing Getting Started Path of a Ball 5 2 Defining and Displaying a Parametric Graph 5 3 Explori...

Страница 94: ...t2 The gravity constant g is 9 8 m sec2 2 Press Press 15 X 60 2 E 1 to select to define the X portion of the parametric equation in terms of T 3 Press 15 W 60 2 E 1 to select c 9 8 e 2 d a to define...

Страница 95: ...also select CONNECTED to obtain a more meaningful parametric graph After selecting PARAM mode press to display the parametric Y edit screen On this screen you display and enter both the X and Y compon...

Страница 96: ...lly Press to display the current Window variable values The Window variables define the viewing window The values shown are the standard values in RADIAN mode TMIN 0 Smallest T value to evaluate TMAX...

Страница 97: ...wing window As a graph is plotted the TI 80 updates X Y and T Note Smart Graph applies to parametric graphs also page 4 11 By means of the VARS WINDOW and Y VARS menus you can Access functions by usin...

Страница 98: ...displays values for X and Y The values for X Y and T are updated as you move the Trace cursor If the cursor moves off the top or bottom of the screen the coordinate values continue to change appropri...

Страница 99: ...the Y list and displays each value for the independent variable along with the evaluated value for each corresponding dependent variable Getting Started Roots of a Function 6 2 Defining the Independe...

Страница 100: ...ny sign changes are there and where do they occur 1 If necessary select FUNC from the MODE menu Press 2 to display the TABLE SETUP screen Press 10 to set TBLMIN L10 Leave TBL 1 2 Press a 4 3 to enter...

Страница 101: ...To change TBLMIN and TBL simply enter the values at the blinking cursor To move between TBLMIN and TBL press 8 and 7 You can also store values to TBLMIN and TBL from the Home screen or a program The...

Страница 102: ...dependent variables in the Y editor FUNC Mode PARAM Mode In PARAM mode you must define both components of the parametric equation Chapter 5 Only functions that are selected are displayed in the table...

Страница 103: ...The bottom line displays the full value of the current cell which is indicated by the rectangular cursor The center portion is used to display the values of the variables abbreviated to six digits if...

Страница 104: ...ore than one function defined and selected press 9 to display other dependent variables In the example below TBLMIN 0 TBL 1 Y1 X2 2 and Y2 X3 2 You can press 9 9 to see the values for Y2 Displaying Ot...

Страница 105: ...ions you should be familiar with Chapter 4 Function Graphing Getting Started Shading a Graph 7 2 DRAW DRAW Menu 7 3 Drawing Lines 7 4 Drawing Horizontal and Vertical Lines 7 5 Drawing a Function 7 6 S...

Страница 106: ...ss 4 to select the ZDECIMAL viewing window clear any existing drawings and display the viewing window and graph 3 Press 2 to return to the Home screen 4 Press 2 F 7 to select SHADE_Y which is copied t...

Страница 107: ...erations draw on top of the graph of currently selected functions you may want to do one or more of the following before drawing on a graph Change the mode settings Enter or edit functions in the Y li...

Страница 108: ...at the beginning point of the line you want to draw Press 3 Move the cursor to the end point of the line you want to draw The line is displayed as you move the cursor Press To continue to draw lines r...

Страница 109: ...the cursor Position the cursor where you want to draw the line Press The line is drawn on the graph To continue to draw lines repeat step 2 To cancel HORIZONTAL or VERTICAL press M HORIZONTAL DRAW DR...

Страница 110: ...unction Y1 5 when you press Note You cannot trace on DRAWF functions GRIDON DRAW DRAW item 9 and GRIDOFF DRAW DRAW item 0 set graphs to be drawn with the grid points on or off respectively The grid po...

Страница 111: ...nction1 function4 When executed SHADE_Y plots the specified function s on the graph and shades the area above the function with a pattern The patterns for shading are automatically assigned in the fol...

Страница 112: ...with a pattern The patterns for shading are automatically assigned in the following order Function 1 Horizontal pattern Function 2 Diagonal pattern upper left to lower right Function 3 Diagonal patte...

Страница 113: ...rfunc are shaded You can specify the shading resolution an integer between 1 and 9 If none is specified 1 is used resolution 1 shades every pixel resolution 2 shades every second pixel resolution 3 sh...

Страница 114: ...PT ON Turn on a point 2 PT OFF Turn off a point 3 PT CHANGE Toggle a point on or off To draw points directly on a graph 1 When a graph is displayed select PT ON from the DRAW POINTS menu item 1 2 Posi...

Страница 115: ...the same as for PT ON When you use these instructions from the Home screen or a program you must specify the X coordinate and the Y coordinate of the point as arguments for the instructions PT ON tur...

Страница 116: ...nd displayed immediately with no drawn elements Note that CLRDRAW gives you a quick way to replot the current graph in addition to clearing the current drawings Begin on a blank line on the Home scree...

Страница 117: ...f the TI 80 The TI 80 can store up to six lists A list depending on available memory can have up to 99 elements Getting Started Generating a Sequence 8 2 About Lists 8 3 LIST OPS Operations 8 6 LIST M...

Страница 118: ...the increment is 1 1 Begin on a blank line on the Home screen Press 2 to display the LIST OPS menu 2 Press 4 to select SEQ The function name is copied to the cursor location on the Home screen 3 Press...

Страница 119: ...be an expression for each element in the list separated by commas 3 Press 2 to indicate the end of the list The expression is evaluated when the entry is executed Commas are required on entry to separ...

Страница 120: ...list followed by the number of the element in parentheses You can store to any element within the currently defined list dimensions or one beyond listname element You can also edit a list by means of...

Страница 121: ...be valid for every element in the list This returns an error because 1 is divided by 0 If two lists are used with a two argument function the lengths of the lists must be the same The answer is a list...

Страница 122: ...g list and update the list in memory With two to six list names they sort the first list and then sort the remaining lists as dependent lists placing their elements in the same order as their correspo...

Страница 123: ...ist are zeros length DIM listname DIM is also used with to redimension an existing list The elements in the old list that are within the new dimension are not changed Any elements in the old list that...

Страница 124: ...t in which each element is the result of the evaluation of expression with regard to variable for values ranging from begin to end at steps of increment SEQ expression variable begin end increment The...

Страница 125: ...IST MATH item 1 or MAX maximum LIST MATH item 2 returns the smallest or largest element of the specified list If two lists are compared it returns a list of the smaller or larger of each pair of eleme...

Страница 126: ...ed list SUM list PROD product LIST MATH item 6 returns the product of the elements of the list PROD list You can combine SUM or PROD with SEQ to obtain upper upper Gexpression x expression x x lower x...

Страница 127: ...g Started Building Height and City Size 9 2 Setting Up a Statistical Analysis 9 8 The STAT List Editor 9 9 Viewing Entering and Editing Lists 9 10 Sorting and Clearing Lists 9 13 Statistical Analysis...

Страница 128: ...Thousands Buildings 12 Stories 150 4 500 31 800 42 250 9 550 20 750 55 1 To clear any existing lists press A 4 to copy CLRLIST to the Home screen 2 Press 2 b 2 b 2 b 2 t The message DONE is displayed...

Страница 129: ...L2 Press 4 31 42 9 20 55 8 You can sort the data by size of city Press 2 M to return to a clear Home screen Press A 2 to select SORTA which is copied to the Home screen Press 2 to select the independ...

Страница 130: ...YPE as scatter plot XL independent list as L1 YL dependent list as L2 and Mark as 12 Press to display the Window variables Enter the following values 0 for XMIN 1000 for XMAX 100 for XSCL L15 for YMIN...

Страница 131: ...ATISTICS and press 9 9 to display the VARS EQ menu 18 Press 5 to select REGEQ which copies the linear regression to the Y editor screen Note Each time you calculate a regression the regression equatio...

Страница 132: ...RS 1 to select Y1 and then press y This defines L as the values predicted by the LINREG line 23 Press to store the values in L3 24 To store the residuals in L4 press to move the cursor onto the name L...

Страница 133: ...nimum and maximum values of L4 M10 31862745 and 10 74019608 as guidelines for setting YMIN and YMAX 29 Press to plot the residuals marks each residual value 30 Press y QUIT M to return to a clear Home...

Страница 134: ...le Follow these basic steps to perform statistical analyses 1 Enter the statistical data in lists pages 9 9 through 9 13 2 Select the type of statistical calculations you want to do pages 9 14 through...

Страница 135: ...er portion displays up to six elements of two lists showing the values of the elements abbreviated to six digits if necessary The full value of the current element indicated by the rectangular cursor...

Страница 136: ...4 Deletes the current list element and closes up the list In the editing context an edit cursor is active on the bottom line and you can change the value of the current list element You can also move...

Страница 137: ...cursor to the element you want to change 3 Press to switch to the editing context Then Change the current value by inserting deleting or typing over digits Press an entry key such as a number or lett...

Страница 138: ...1 Press A Enter several elements in L1 2 Press 7 and 9 as many times as necessary to move the cursor to the list name L2 3 Press 2 p 2 This is the expression that will define the elements in L2 4 Pre...

Страница 139: ...h two to six list names they sort the first list and then sort the remaining lists as dependent lists placing their elements in the same order as their corresponding elements in the first list This le...

Страница 140: ...ed in the calculation If you enter more than one list name separate them by commas 3 Press to perform the calculation and display the results For all of the calculation types you can include a list of...

Страница 141: ...stname 2 VAR STATS two variable statistics STAT CALC item 2 analyzes paired data between which there is a relationship This option calculates statistical results as indicated on page 9 17 The first li...

Страница 142: ...quation y a b ln x using a least squares fit and transformed values LN x and y It displays a b and r correlation coefficient LNREG Xlistname Ylistname LNREG Xlistname Ylistname freqlistname EXPREG exp...

Страница 143: ...values X Y MAXX maximum of X values X Y MINY minimum of Y values X Y MAXY maximum of Y values X Y Q1 1st quartile BOX MED median BOX Q3 3rd quartile BOX a b regression fit coefficients EQ a b c quadra...

Страница 144: ...lect or deselect Y equations as appropriate Chapter 4 4 Define the statistical plot page 9 20 5 Turn the plot s on if necessary page 9 21 6 Define the viewing window page 9 21 and Chapter 4 7 Display...

Страница 145: ...When three are plotted the first plots at the top the second in the middle and the third at the bottom histogram plots one variable data XSCL determines the width of each bar beginning at XMIN XMAX X...

Страница 146: ...ely select ON You can define a plot at any time and leave it OFF The definition will be available in the future 4 Select the type of plot The options change appropriately scatter plot XL YL MARK XYLin...

Страница 147: ...t graph You may define the viewing window by pressing and then entering values for the Window variables When you trace a scatter plot or XYLine tracing begins at the first element in the lists When yo...

Страница 148: ...program editor select the type of calculation from the STAT CALC menu 2 Enter the names of the lists separated by commas to use in the calculation Note To display a regression equation and coefficient...

Страница 149: ...9 to display the TYPE menu Select the type of plot scatter XYLine box or histogram is copied to the cursor location 4 Press b Enter the list names separated by commas 5 This step is for and only Pres...

Страница 150: ...9 24 Statistics To display a plot use any of the Zoom instructions Chapter 4 or use the DISPGRAPH instruction Chapter 10 Displaying a Stat Plot from a Program...

Страница 151: ...and execute programs on the TI 80 Getting Started Rolling a Die 10 2 About TI 80 Programs 10 4 Creating and Executing Programs 10 5 Editing Programs 10 6 PRGM CTL Control Instructions 10 7 PRGM I O I...

Страница 152: ...n the program editor The colon in the first column of the second line indicates that this is the beginning of a command line 3 Press K 9 to access the PRGM I O menu Press 4 CLRHOME is copied to cursor...

Страница 153: ...roll in L1 Press to complete the instruction 9 Press K 6 to select PAUSE which is copied to the cursor location This pauses the program after displaying the result of the last roll Press to complete...

Страница 154: ...grams Storing a new value to a variable or list in a program changes the value in memory during program execution As calculations are made in programs the TI 80 updates ANS just as it would if the cal...

Страница 155: ...mmand is longer than one line on the screen it wraps to the next line 2 6 and 2 9 move the cursor to the beginning and end of a command line In the program editor if you press a key that accesses a me...

Страница 156: ...tion the cursor and then make the changes by typing over the command or using 4 or 2 Press M to clear blank all program commands on the command line The leading colon is not deleted and then enter a n...

Страница 157: ...BL Defines a label 8 GOTO Goes to a label 9 PRGM_ Executes a program as a subroutine 0 RETURN Returns from a subroutine A STOP Stops program execution Program control instructions tell the TI 80 which...

Страница 158: ...em 5 identifies the end of the group IF condition THEN command if true END command ELSE PRGM CTL item 3 following IF THEN executes a group of commands if the condition is false zero END PRGM CTL item...

Страница 159: ...END identifies the end of the loop FOR loops can be nested FOR variable begin end increment command while end not exceeded END command END PRGM CTL item 5 identifies the end of a group of commands Eac...

Страница 160: ...created When encountered the command executes the specified program and then returns to the calling program Execution continues with the command following PRGM_programname PRGM_programname RETURN PRGM...

Страница 161: ...cursor location CTL I O EXEC 1 INPUT Enters a value or displays the current graph 2 DISP Displays text value or the Home screen 3 DISPGRAPH Displays the current graph 4 CLRHOME Clears the Home screen...

Страница 162: ...tion INPUT variable INPUT listname INPUT Yname You can enter a string of up to 16 characters to prompt for the value to be entered During program execution enter a value and press after the prompt The...

Страница 163: ...P ANSWER IS p 2 displays If PAUSE is encountered after DISP the program halts temporarily so that you can examine the screen Press to resume program execution Note A statement that results in a value...

Страница 164: ...s encountered during program execution the next command that the program executes is the first command in the second program Execution continues with the subsequent command in the first program when i...

Страница 165: ...nd Spinners 11 2 The Unit Circle and Trigonometric Curves 11 3 Program Newton s Numerical Solve Routine 11 4 Program Numerical Integration 11 6 Program Window Variables Store and Recall 11 8 Graphing...

Страница 166: ...xperiment enter RANDINT 0 1 from the Home screen 0 tails and 1 heads Press repeatedly to generate the coin tosses You can also write a simple program to display heads or tails for each coin toss You c...

Страница 167: ...ing this procedure to solve the problem 1 Press 3 and select RADIAN PARAM and SIMUL 2 Press and set the Window variables TMIN 0 XMIN 2 YMIN 3 TMAX 2p XMAX 2p YMAX 3 TSTEP 1 XSCL p 2 YSCL 1 3 Press and...

Страница 168: ...and trace the function and then enter X as the guess PROGRAM NEWTON INPUT INITIAL X X Input initial guess LBL N Begin loop X Y1 NDERIV Y1 X X R Calculate new root DISP R PAUSE IF ABS X R ABS X 1 10 Te...

Страница 169: ...me screen execute the program NEWTON 7 Enter X as the initial guess and press repeatedly The program stops when the relative difference between the new root estimate and the previous root estimate is...

Страница 170: ...MIT A Input lower limit INPUT UPPER LIMIT B Input upper limit INPUT N DIVISIONS D Input of divisions 0 S Initialize sum variable B A 2 D W Calculate division width FOR J 1 D 1 Begin calculation loop A...

Страница 171: ...Set the Window variables 4 Execute the program SIMPSON from a clear Home screen entering the limits and divisions as you are prompted 5 You can display the calculated area graphically using SHADE from...

Страница 172: ...STORE WINDOW DISP 2 RECALL WINDOW DISP 3 QUIT DISP DISP ENTER 1 2 OR 3 INPUT M Present menu of choices IF M 1 GOTO S IF M 2 GOTO R GOTO Q Evaluate menu selection LBL S XMIN A XMAX B XSCL C YMIN D YMAX...

Страница 173: ...lank Home screen The program prompts with three options Store the Window variables you are currently using View a graph using a previously stored set of Window variables Quit the program 2 Press 1 2 o...

Страница 174: ...form as XT F T and YT T For example Y 2X3 2X 6 would be expressed as XT 2T3 2T 6 and YT T Graph the function Y 2X3 2X 6 and its inverse Follow this procedure to solve the problem 1 Select Param CONNE...

Страница 175: ...the graph of the function through the line Y X produces the graph of its inverse X3 T Y3 T 6 Press to plot the graph Press and then press 9 several times until the cursor appears Next press 8 and 7 s...

Страница 176: ...s 3 and select FUNC 2 Enter the first piece of the function in the Y editor This piece is f x x for x 3 It is entered as x x 3 Y is then equivalent to x 1 for x 3 and x 0 for x 3 3 Add the second piec...

Страница 177: ...function is then equivalent to 6 x 1 When X is less than 5 the test x 5 returns 0 The third piece of the function is then equivalent to 6 x 0 5 Enter these Window variable values Xmin 2 Ymin 2 Xmax 8...

Страница 178: ...nequality as Y1 the right side as Y2 and the statement of the inequality as Y3 Y3 evaluates to 1 if true and 0 if false 3 Press and enter these Window variable values Xmin 10 Ymin 10 Xmax 10 Ymax 10 X...

Страница 179: ...q sin q Thus the Spiral of Archimedes can be expressed parametrically as x 5 q cos q y 5 q sin q Follow this procedure to solve the problem 1 Select PARAM mode Choose the defaults for the other mode s...

Страница 180: ...XMAX p 2 XSCL 10 YMIN 10 YMAX 1 YSCL Set viewing window A SIN BX Y1 RANDINT 1 10 A RANDINT 1 10 B Initialize coefficients PLOTSOFF FNOFF DISPGRAPH SEQ XMIN I X I 0 62 9 L1 Y1 L1 L2 PLOT1 L1 L2 DISPGR...

Страница 181: ...of memory available for use occasionally you may want to delete stored items that you are no longer using You can also reset the calculator erasing all data and programs Checking Available Memory 12 2...

Страница 182: ...nd the amount used by old items that you no longer need To check the amounts of available and used memory 1 Press 2 to display the MEMORY menu 2 Press 1 or to select CHECK RAM The amount of available...

Страница 183: ...ogram names List names Y equation names Numeric variable names 3 Use 7 and 8 to position the cursor which is indicated by in the left column next to the item you want to delete and press The item is d...

Страница 184: ...80 To reset the TI 80 1 Press 2 to display the MEMORY menu 2 Press 3 to select RESET 3 Make the appropriate menu selection To go to the Home screen without resetting memory select NO To reset memory s...

Страница 185: ...can use in expressions and instructions that you can use on the Home screen and in programs It also includes other reference information that can help you Table of TI 80 Functions and Instructions A...

Страница 186: ...ent in list F 2 P 2 6 Addition valueA valueB Returns valueA plus valueB F 2 4 Addition value list Returns a list in which value is added to each list element F 2 4 Addition listA listB Returns a list...

Страница 187: ...value F I MATH 2 8 Cube Root list Returns a list of the cube root for each list element F I MATH 2 8 value8DEC Returns value in decimal form I I MATH 4DEC 2 8 list8DEC Returns list in decimal form I...

Страница 188: ...sed to the value of power F 2 s 2 5 e list Returns a list of e raised to the power of each list element F 2 s 2 5 ELSE See IF THEN ELSE END Identifies the end of a FOR IF THEN or IF THEN ELSE structur...

Страница 189: ...s fixed decimal display mode for n decimal places I 3 FIX 1 10 FLOAT Sets floating decimal display mode I 3 FLOAT 1 10 FNOFF Deselects all Y functions I 2 G ON OFF FNOFF 4 8 FNOFF function function De...

Страница 190: ...urns 1 if valueA valueB Returns 0 if valueA valueB F 2 D 2 16 Greater Than listA listB Applies the test to each element of listA and listB and returns a list F 2 D 2 16 Greater Than list value or valu...

Страница 191: ...variable Prompts for input to store to variable I K I O INPUT 10 12 INPUT text variable Prompts using text and stores input to variable I K I O INPUT 10 12 INT value Returns the largest integer value...

Страница 192: ...alueA valueB F 2 D 2 16 Less Than or Equal listA listB Applies the test to each element of listA and listB and returns a list F 2 D 2 16 Less Than or Equal list value or value list Applies the test to...

Страница 193: ...MATH MAX 8 9 MAX list Returns the largest element in list F 2 MATH MAX 8 9 MAX listA listB Returns a list of the larger of each pair of elements in listA and listB F 2 MATH MAX 8 9 MAX list value or...

Страница 194: ...0 taken valueB integer 0 at a time F I PRB nCr 2 13 value nCr list Returns a list of the combinations of value integer 0 taken each element in list integer 0 at a time F I PRB nCr 2 13 list nCr value...

Страница 195: ...integer 0 taken valueB integer 0 at a time F I PRB nPr 2 13 value nPr list Returns a list of the permutations of value integer 0 taken each element in list integer 0 at a time F I PRB nPr 2 13 list nP...

Страница 196: ...I 2 PLOTn 9 20 PLOTSOFF Deselects all stat plots I 2 PLOTSOFF 9 21 PLOTSOFF plot plot Deselects stat plot1 plot2 or plot3 I 2 PLOTSOFF 9 21 PLOTSON Selects all stat plots I 2 PLOTSON 9 21 PLOTSON plo...

Страница 197: ...a list of x coordinates given the R and q coordinates in Rlist and qlist F 2 E P4Ry 2 15 P8Ry R q Returns rectangular coordinate y given polar coordinates R and q F 2 E P4Ry 2 15 P8Ry Rlist q Returns...

Страница 198: ...ue as an angle in radians 2 E r 2 14 RAND Returns a random number between 0 and 1 F I PRB RAND 2 12 RANDINT lower upper Returns a random integer between lower and upper F I PRB RANDINT 2 13 RANDINT lo...

Страница 199: ...of value F I MATH x 2 8 listAx listB Returns a list of listA roots of listB F I MATH x 2 8 ROUND value Returns value rounded to 10 digits F I NUM ROUND 2 10 ROUND value decimals Returns value rounded...

Страница 200: ...ates given the X coordinates in Xlist and the Y coordinates in Ylist F 2 E R4Pq 2 15 SCI Sets scientific display mode I 3 SCI 1 10 seq expression variable begin end increment Returns a list created by...

Страница 201: ...I 2 F DRAW SHADE_Y 7 8 fraction SIMP Simplifies fraction by its lowest common factor F J SIMP 3 8 fraction factor SIMP Simplifies fraction by the specified factor which must be an integer F J SIMP 3...

Страница 202: ...F 2 2 5 STOP Stops program execution and returns to the Home screen I K CTL STOP 10 10 Store value variable Stores value to variable I 1 13 Store list listname Stores list to listname I 1 13 Store exp...

Страница 203: ...freqlistname Performs two variable analysis using Xlistname and Ylistname with frequency freqlistname I A CALC 2 VAR STATS 9 15 VERTICAL X Draws a vertical line at value X I 2 F DRAW VERTICAL 7 5 ZBOX...

Страница 204: ...2p TSTEP p 24 XMIN 10 XMAX 10 XSCL 1 YMIN 10 YMAX 10 YSCL 1 2 TblSet TABLE SETUP TBLMIN 0 TBL 1 ZOOM 1 ZBOX 2 ZOOM IN 3 ZOOM OUT 4 ZDECIMAL 5 ZSQUARE 6 ZSTANDARD 7 ZTRIG 3 3 in program editor NORMAL S...

Страница 205: ...3 PLOT3 4 PLOTSOFF 5 PLOTSON TYPE 1 2 3 4 MARK 1 2 3 Screen for or plots 1 variable plots PLOTn ON OFF TYPE XL L1L2L3L4L5L6 F 1L1L2L3L4L5L6 Screen for or plots 2 variable plots PLOTn ON OFF TYPE XL L1...

Страница 206: ...2 MAX 3 MEAN 4 MEDIAN 5 SUM 6 PROD I MATH 1 INT 2 4DEC 3 3 4 3 5 X 6 NDERIV NUM 1 ROUND 2 IPART 3 FPART 4 INT 5 MIN 6 MAX 7 REMAINDER PRB 1 RAND 2 nPr 3 nCr 4 5 RANDINT J 2 D 2 E FRACTION 1 4SIMP 2 4b...

Страница 207: ...ame NEW 1 CREATE NEW CTL 1 IF 2 THEN 3 ELSE 4 FOR 5 END 6 PAUSE 7 LBL 8 GOTO 9 PRGM_ 0 RETURN A STOP I O 1 INPUT 2 DISP 3 DISPGRAPH 4 CLRHOME EXEC 1 name 2 name 3 name 2 F DRAW 1 CLRDRAW 2 LINE 3 HORI...

Страница 208: ...YSCL 7 X 8 Y 9 XFACT 0 YFACT T 1 TMIN 2 TMAX 3 TSTEP TABLE 1 TBLMIN 2 TBL L SIMPFACTOR SIMPFACTOR 1 FACTOR L STATISTICS X Y 1 n 2 v 3 Sx 4 sx 5 w 6 Sy 7 sy 8 MINX 9 MAXX 0 MINY A MAXY G 1 GX 2 GX 3 GY...

Страница 209: ...3 RESET 2 CHECK RAM 2 DELETE 2 RESET MEM FREE 7014 REAL 14 LIST 0 Y VARS 80 PRGM 14 DELETE name memory name memory name memory names include defined programs lists Y equations and user variables in th...

Страница 210: ...store any string of characters functions instructions or variable names to the functions Yn in FUNC mode and Xn and Yn in PARAM mode by using either or the Y editor The validity of the string is dete...

Страница 211: ...se the TI 80 It includes procedures that may help you correct problems with the calculator Battery Information B 2 Accuracy Information B 8 In Case of Difficulty B 10 Error Conditions B 11 Service and...

Страница 212: ...diagrams carefully Do not replace batteries with rechargeable batteries Do not place non rechargeable batteries in a battery charger Properly dispose of used batteries immediately Do not leave them w...

Страница 213: ...e keys c Turn the calculator so that the back is facing you Placing your thumb on the ridged area of the plastic battery compartment cover push down slightly and slide the cover to the right until you...

Страница 214: ...l battery cover away from the battery The battery pops up Remove the old battery Insert a new battery positive side up Hold the new battery in place and slide the metal battery cover back into positio...

Страница 215: ...Push the red switch all the way down to free the metal battery cover over the upper battery Slide the metal battery cover away from the battery Remove the old battery Insert a new battery positive sid...

Страница 216: ...de the metal battery cover back into position over the battery Push the red switch to its center position to lock the metal covers and batteries into place Note The calculator will not turn on unless...

Страница 217: ...t cover Turn the calculator on and adjust the contrast display To adjust the display contrast press and release the 2 key To increase the contrast darken the screen press and hold 7 To decrease the co...

Страница 218: ...s the center of the next to the rightmost pixel The rightmost pixel is reserved for the busy indicator X is the distance between the centers of two adjacent pixels X is calculated as XMAX XMIN 62 If X...

Страница 219: ...010 degree SIN 1 x COS 1 x 1 x 1 LN x LOG x 10 100 x 10100 ex 10100 x 230 2585092993 10x 10100 x 100 x 0 x 10100 x 0 x 69 where x is an integer Following is a table of functions and the range of the r...

Страница 220: ...not appear to be working at all be sure the batteries are installed properly and that they are fresh Refer to Battery Information beginning on page B 2 for more details Note Make sure the red switch...

Страница 221: ...invalid data type for example a list where a real number is required See Appendix A and the appropriate chapter You are attempting to store to an incorrect data type for example a list to a real varia...

Страница 222: ...ABEL The label in the GOTO instruction is not defined with a LBL instruction in the program MEMORY There is insufficient memory in which to perform the desired command You must delete item s from memo...

Страница 223: ...ntains a syntax error Look for misplaced functions arguments parentheses or commas See Appendix A and the appropriate chapter UNDEFINED You are attempting to reference a variable that is not currently...

Страница 224: ...omers outside the U S Canada Puerto Rico and the Virgin Islands Contact TI by e mail or visit the TI calculator home page on the World Wide Web e mail ti cares ti com Internet education ti com Product...

Страница 225: ...PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS EXPENSES OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER Some states provinces do not allow the exclusion or limitation of implied warranties...

Страница 226: ...r or any other user Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages so the above limitations or exclusions may not apply to you Legal Remedie...

Страница 227: ...ng a graph 7 2 Unit circle and trig curves 11 3 Windows variables store and recall 11 8 to 11 9 Working with fractions 3 2 to 3 3 Arcsine arccosine arctangent See SIN 1 COS 1 TAN 1 Argument x A Cont A...

Страница 228: ...3 Dimension list 8 6 8 7 A 3 DIM MISMATCH error B 11 DISP 10 3 10 11 10 13 A 3 DISPGRAPH 9 24 10 11 10 13 A 3 Display 1 4 1 5 contrast 3 1 3 B 2 B 10 cursors 1 5 1 8 decimal 2 8 A 3 fraction 3 8 3 10...

Страница 229: ...A 6 Functions x 1 6 1 7 2 3 B 9 clearing 4 6 editing 4 6 entering 4 7 defining 4 5 4 6 5 3 evaluating 4 7 graphing 4 2 to 4 18 parametric 5 2 to 5 6 selecting 4 8 5 4 G Getting Started See Applicatio...

Страница 230: ...0 2 11 8 9 A 9 Maximum 2 10 2 11 8 9 9 17 9 19 9 21 M Cont MAXX MAXY 9 17 9 19 9 21 MEAN 8 9 A 9 MED 9 17 9 19 9 21 A 26 MEDIAN 8 9 A 9 Median point 9 17 MEMORY error B 12 MEMORY menu 12 2 to 12 4 MEM...

Страница 231: ...2 PRB MATH menu 2 12 2 13 PRGM_ 10 7 10 10 10 14 A 13 PRGM CTL menu 10 7 to 10 10 P Cont PRGM EXEC menu 10 5 10 14 PRGM EDIT menu 10 6 PRGM I O menu 10 11 to 10 13 PRGM NEW menu 10 2 10 5 Probability...

Страница 232: ...n 9 17 Standard Window 4 2 4 9 4 15 4 17 A 19 STAT error B 13 STAT CALC menu 9 14 to 9 17 S Cont STAT EDIT menu 9 9 to 9 13 STAT list editor 9 2 to 9 7 9 9 to 9 13 STAT MARK menu 9 20 9 23 STAT PLOT e...

Страница 233: ...4 12 4 17 5 2 5 4 9 19 A 26 B 8 B 12 B 13 X Y VARS menu 1 19 9 17 XYLINE 9 18 9 20 9 21 Y w 9 17 A 26 Y 4 11 to 4 13 A 26 B 11 Y Cont Y VARS menu 1 19 Yn 1 19 4 5 to 4 7 10 12 A 26 Y1 Y2 Y3 9 14 9 15...

Страница 234: ...STAT PLOT FRAC TI 80 E b X T c x x x x...

Страница 235: ......

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