K quadratic differential calculations – Casio SERIES FX-9860G User Manual
Page 102
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k Quadratic Differential Calculations
[OPTN]-[CALC]-[
d
2
/
dx
2
]
After displaying the function analysis menu, you can input quadratic differentials using the
following syntax.
K4(CALC)3(
d
2
/
dx
2
)
f
(
x
),
a
, tol)
(
a
: differential coeffi cient point,
tol
: tolerance)
Quadratic differential calculations produce an approximate differential value using the
following second order differential formula, which is based on Newton’s polynomial
interpretation.
In this expression, values for “suffi ciently small increments of
h” are used to obtain a value
that approximates
f ”( a).
Example
To determine the quadratic differential coeffi cient at the point where
x
= 3 for the function
y
=
x
3
+ 4
x
2
+
x
– 6
Here we will use a tolerance
tol
= 1
E
– 5
Input the function
f(
x
).
AK4(CALC)3(
d
2
/
dx
2
)
vMd+
evx+v-g,
Input 3 as point
a
, which is the differential coeffi cient point.
d,
Input the tolerance value.
bE-f)
w
d
2
d
2
––– ( f (x), a)
⇒ ––– f(a)
dx
2
dx
2
d
2
d
2
––– ( f (x), a)
⇒ ––– f(a)
dx
2
dx
2
f ''(a)
=
180h
2
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)
=
180h
2
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)
2-5-5
Numerical Calculations
# In the function
f
(
x
), only X can be used as
a variable in expressions. Other variables
(A through Z excluding X,
r
,
Ƨ
) are treated
as constants, and the value currently
assigned to that variable is applied during the
calculation.
# Input of the tolerance (
tol
) value and the closing
parenthesis can be omitted.
# Specify a tolerance (
tol
) value of 1
E
-14 or
greater. An error (Time Out) occurs whenever
no solution that satisfi es the tolerance value can
be obtained.