Quadratic Differential Calculations - Casio fx-9860G AU User Manual

k k k k k Quadratic Differential Calculations
After displaying the function analysis menu, you can input quadratic differentials using the
following syntax.
K4(CALC)3(
––– (f (x), a) ⇒ ––– f (a)
dx
Quadratic differential calculations produce an approximate differential value using the
following second order differential formula, which is based on Newton's polynomial
interpretation.
2 f(a + 3h) – 27 f(a + 2h) + 270 f(a + h) – 490 f(a)+270 f(a – h) – 27 f(a – 2h) +2 f(a – 3h)
f''(a) –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
=
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
Here we will use a tolerance tol = 1
Input the function f(
AK4(CALC)3(
evx+v-g,
Input 3 as point
d,
Input the tolerance value.
bE-f)
w
# In the function f(x), only X can be used as a
variable in expressions. Other variables (A
through Z excluding X, r, θ ) are treated as
constants, and the value currently assigned to
that variable is applied during the calculation.
Numerical Calculations
2
d dx
/
a
differential coefficient point , tol: tolerance)
( :
2 2
d d
2 2
dx
y
= 3 for the function
x
).
d
a
, which is the differential coefficient point.
2-5-5
2
f(x) , a ,tol)
)
2
180h
x x x
3 2
= + 4 + – 6
– 5
E
dx ) vMd+
2 2
/
# Input of the tolerance (tol) value and the closing
parenthesis can be omitted.
# Specify a tolerance (tol) value of 1
An error (Time Out) occurs whenever no solution
that satisfies the tolerance value can be obtained.
20050401 20070101
[OPTN]-[CALC]-[d 2 /dx
-14 or greater.
E
2 ]