K differential calculations – Casio fx-115ES User Manual
Page 38
E-36
k Differential Calculations
Your calculator performs differential calculations by approximating
the derivative based on centered difference approximation.
d
/
dx
(
f
(
x
),
a
,
tol
)
f
(
x
): Function of X (All non-X variables are treated as
constants.)
a
:
Input a value to specify the point for which the derivative
should be obtained (differential point)
tol
: Tolerance range (input/output format: Linear)
• You can omit specification of the tolerance range. A default value
of 1
× 10
–10
is used when you do.
•
∫
(,
d
/
dx
(, Pol(, Rec(, and
Σ
( cannot be used within
f
(
x
),
a
, or
tol
.
• Differential calculations can be performed in the COMP Mode only.
• When performing a differential calculation involving trigonometric
functions, specify Rad as the calculator’s default angle unit.
• A “Time Out” error occurs when a differential calculation ends
without the ending condition being fulfilled.
• A smaller
tol
value provides better precision, but it also causes
the calculation to take more time. Specify a
tol
value that is 1
×
10
–14
or greater.
• You cannot input a
tol
value when using Math format.
• Inaccurate results and errors can be caused by the following :
- discontinuous points in
x
values
- extreme changes in
x
values
- inclusion of the local maximum point and local minimum point in
x
values
- inclusion of the inflection point in
x
values
- inclusion of undifferentiable points in
x
values
- differential calculation results approaching zero
• Pressing A will interrupt an ongoing differential calculation.
Appendix
<#033> Determine
f
’(
) when
f
(
x
) = sin(
x
)
(
tol
specification omitted.)
<#034> (3
x
2
– 5
x
+ 2, 2, 1
×10
–12
) = 7
π
2
d
dx