Chapter 2: Main Application
66
u
Π
[Action][Calculation][
Π
]
Function: Evaluates an expression at discrete variable values within a range, and then calculates a product.
Syntax:
Π
(Exp/List, variable, lower value, upper value [ ) ]
Example: To calculate the product of
x
2
as the value of
x
changes from
x
= 1
through
x
= 5
u
rangeAppoint
[Action][Calculation][rangeAppoint]
Function: Finds an expression or value that satisfies a condition in a specified range.
Syntax: rangeAppoint (Exp/Eq/List, start value, end value [ ) ]
• When using an equation (Eq) for the first argument, input the equation using the syntax Var = Exp.
Evaluation will not be possible if any other syntax is used.
Example: To find the expression(s) in the list {
x
=
π
,
x
= 2
π
,
x
= 3
π
} that belong(s) to the closed range 0
s
x
s
5
u
mod
[Action][Calculation][mod]
Function: Returns the remainder when one expression is divided by another expression.
Syntax: mod ({Exp/List} -1, {Exp/List} -2 [ ) ]
Example: To determine the remainder when 26 is divided by 3 (26mod3)
u
tanLine
[Action][Calculation][line][tanLine]
Function: Returns the right side of the equation for the tangent line (
y
= ‘expression’) to the curve at the
specified point.
Syntax: tanLine (Exp/List, variable, variable value at point of tangency [ ) ]
Example: To determine the function of the line tangent to
y
=
x
3
at
x
= 2
u
normal
[Action][Calculation][line][normal]
Function: Returns the right side of the equation for the line normal (
y
= ‘expression’) to the curve at the
specified point.
Syntax: normal (Exp/List, variable, variable value at point of normal [ ) ]
Example: To determine the function of the line normal to
y
=
x
3
at
x
= 2
u
arcLen
[Action][Calculation][line][arcLen]
Function: Returns the arc length of an expression from a start value to an end value with respect to a
specified variable.
Syntax: arcLen (Exp/List, variable, start value, end value [ ) ]
Example: To determine the arc length for
y
=
x
3
2
from
x
= 0 to
x
= 4
u
fMin
[Action][Calculation][fMin/fMax][fMin]
, fMax
[Action][Calculation][fMin/fMax][fMax]
Function: Returns the minimum (fMin) / the maximum (fMax) point in a specific range of a function.
Syntax: fMin(Exp[,variable] [ ) ]
fMin(Exp, variable, start value, end value[,
n
] [ ) ]
fMax(Exp[,variable] [ ) ]
fMax(Exp, variable, start value, end value[,
n
] [ ) ]
• “
x
” is the default when you omit “[,variable]”.
• Negative infinity and positive infinity are the default when the syntax fMin(Exp[,variable] [ ) ] or
fMax(Exp[,variable] [ ) ] is used.
