Casio fx-9860G SD User Manual page 99

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) ––– ( f (x), a) ⇒ ––– f (a)
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) 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) 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
Input the function f(
AK4(CALC)3(
evx+v-g,
Input 3 as point
d,
Input the tolerance value.
bE-f)
w
f x
# In the function ( ), only X can be used as
a variable in expressions. Other variables
(A through Z excluding X,
as constants, and the value currently
assigned to that variable is applied during the
calculation.
Numerical Calculations
d dx
/
2
a
( : differential coefficient point,
d d d d
2 2 2 2
dx dx dx dx
2 2 2 2
y
= 3 for the function
x
).
d
a
, which is the differential coefficient point.
r θ
, ) are treated
2-5-5
f x a
) ( ),
2
,tol)
tol
180h 180h
2 2
x x x
= + 4 + – 6
3 2
tol
= 1 – 5
E
dx
/ ) vMd+
2 2
# Input of the tolerance (
parenthesis can be omitted.
# Specify a tolerance (
greater. An error (Time Out) occurs whenever
no solution that satisfies the tolerance value can
be obtained.
20061001 20070101
d
2
[OPTN]-[CALC]-[
: tolerance)
tol
) value and the closing
tol
) value of 1 -14 or
E
dx
/
2
]