Casio ALGEBRA FX 2.0, Руководство пользователя

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19990401
k k
k k k
Quadratic Differential Calculations
[OPTN] - [CALC] - [
d 2
/
dx 2
]
After displaying the function analysis menu, you can input quadratic differentials using either of
the two following formats.
K 4
(CALC)
c
(
d
2 /
dx
2
)
f ( x )
,
a
,
tol
)
Quadratic differential calculations produce an approximate differential value using the follow-
ing second order differential formula, which is based on Newton's polynomial interpretation.
2 f ( a + 3 h ) – 27 f ( a + 2 h ) + 270 f ( a + h ) – 490 f ( a )+270 f ( a – h ) – 27 f ( a – 2h ) +2 f ( a – 3 h )
f ''
(
a
)
=
–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
180
h 2
In this expression, values for “sufficiently small increments of h ” are used to obtain a value that
approximates f ”( a ).
Example To determine the quadratic differential coefficient at the point where
x
= 3 for the function
y
=
x
3
+ 4
x
2
+
x
– 6
Here we will use a tolerance tol = 1
E
– 5
Input the function
f (
x
)
.
A K 4
(CALC)
c
(
d
2
/
dx
2
)
v M d+
e vx + v -g,
Input 3 as point
a
, which is differential coefficient point.
d,
Input the tolerance value.
b E- f)
w
2-5-5
Numerical Calculations
# In the function
f ( x )
, only X can be used as a
variable in expressions. Other variables (A
through Z,
r
,
"
) are treated as constants, and
the value currently assigned to that variable is
applied during the calculation.
# Input of the tolerance (
tol
) value and the closing
parenthesis can be omitted.
# Discontinuous points or sections with drastic
fluctuation can adversely affect precision or
even cause an error.
(
a
:
differential coefficient point ,
tol
: tolerance)
d 2 d 2
––– ( f ( x ), a )
&
––– f ( a )
dx
2
dx
2