Quadratic Differential Calculations - Casio FX-9750G plus User Manual

3-3 Quadratic Differential Calculations

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After displaying the function analysis menu, you can input quadratic differentials
using either of the two following formats.
d dx
2 / 2
)
3(
d
2
––– ( f (x), a, n) ⇒ ––– f (a)
dx 2
Quadratic differential calculations produce an approximate differential value using
the following second order differential formula, which is based on Newton's
polynomial interpretation.
f(x – 2h) + 16 f(x – h) – 30 f(x) + 16 f(x + h) – f(x + 2h)
–
f''(x) –––––––––––––––––––––––––––––––––––––––––––––––
=
In this expression, values for "sufficiently small increments of
calculated using the following formula, with the value of
= 1, 2, 3 and so on.
1
h = ––––
5
m
The calculation is finished when the value of
calculated using the last value of
h
calculated using the current value of
reached.
• Normally, you should not input a value for
n
input a value for
• Inputting a larger value for
u u u u u To perform a quadratic differential calculation
Example To determine the quadratic differential coefficient at the point
where
Here we will use a final boundary value of n = 6.
x
Input the function f(
AK4(CALC)3(
evx+v-g,
manuals search engine
f(x) a n
, , )
Final boundary (
Differential coefficient point
d
2
dx 2
12h
m
, and the value of
m
are identical before the upper
when required for calculation precision.
n
does not necessarily produce greater precision.
x y
= 3 for the function
).
d dx
/ ) vMd+
2 2
[OPTN]-[CALC]-[d
n
= 1 to 15)
2
x
" are sequentially
m
being substituted as
f " (x)
based on the value of
f " (x)
based on the value of
n
. It is recommended that you only
x x x
= + 4 + – 6
3 2
/dx ]
2 2
m
h
n
digit is