Differential Calculations - Casio fx-9750GII User Manual

Differential Calculations

To perform differential calculations, first display the function analysis menu, and then input the
values using the syntax below.
(CALC)*
a
( : point for which you want to determine the derivative,
d/dx ( f (x) , a) d/dx ( f (x) , a)
The differentiation for this type of calculation is defined as:
f (a + A x) – f (a) f (a + A x) – f (a)
f (a) = lim –––––––––– ––– f (a) = lim –––––––––– ––– ' '
A x 0 A x 0
In this definition, infinitesimal is replaced by a sufficiently small
f '
neighborhood of
f (a + A x) – f (a) f (a + A x) – f (a)
f (a) f (a) ' ' –––––––––– ––– –––––––––– –––
In order to provide the best precision possible, this unit employs central difference to perform
differential calculations.
Example To determine the derivative at point
y
=
f
Input the function (
x a
Input point = for which you want to determine the derivative.
Input the tolerance value.
Using Differential Calculation in a Graph Function
• Omitting the tolerance (
function simplifies the calculation for drawing the graph. In such a case, precision is
sacrificed for the sake of faster drawing. The tolerance value is specified, the graph is drawn
with the same precision obtained when you normally perform a differential calculation.
• You can also omit input of the derivative point by using the following format for the differential
d dx
graph: Y2= / (Y1). In this case, the value of the X variable is used as the derivative point.
Differential Calculation Precautions
f x
• In the function (
(A through Z excluding X,
that variable is applied during the calculation.
• Input of the tolerance (
tol
tolerance ( ) value, the calculator automatically uses a value for
• Specify a tolerance (
solution that satisfies the tolerance value can be obtained.
• Pressing during calculation of a differential (while the cursor is not shown on the display)
interrupts the calculation.
d dx f x a tol
( / ) ( )
d d
f (a) f (a)
dx dx
A x A x
a
( ) calculated as:
A x A x
x x x
3 + 4 2 + – 6, with a tolerance of "
x
).
(CALC)*
tol
) value when using the differential command inside of a graph
), only X can be used as a variable in expressions. Other variables
r
, ) are treated as constants, and the value currently assigned to
tol
) value and the closing parenthesis can be omitted. If you omit
tol
) value of 1 –14 or greater. An error (Time Out) occurs whenever no
E
x
= 3 for the function
tol
d dx
( / )
2-24
[OPTN]-[CALC]-[
II
* fx-7400G
tol
: tolerance)
x
, with the value in the
" = 1 – 5
E
II
* fx-7400G
tol
as 1 –10.
E
d dx
/ ]
: (CALC)
: (CALC)