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Computer Algebra System (CAS) 14-25
Typing:
gives:
• Example — Expansion in the vicinity of x=+∞
or x=–∞
Example 1
Give a 5th-order expansion of arctan(x) in the vicinity of
x=+∞, taking as infinitely small .
Typing:
SERIES(ATAN(X),X =+∞,5)
gives:
Example 2
Give a 2nd-order expansion of in the
vicinity of x=+∞, taking as infinitely small .
gives:
• Unidirectional expansion
To perform an expansion in the vicinity of x = a where
x > a, use a positive real (such as 4.0) for the order.
To perform an expansion in the vicinity of x = a where
x < a, use a negative real (such as –4.0) for the order.
S
ERIES COS 2 X⋅()
2
X
π
6
---
=4,,
⎝
⎠
⎛
⎞
1
4
---
3h 2h
2 83
3
----------
h
3 8
3
---
h
4
0
h
5
4
-----
⎝⎠
⎛⎞
+–++–
hX
π
6
---
–=
〈|〉
h
1
x
---
=
π
2
---
⎝
⎛
h
h
3
3
-----
h
5
5
-----
0
π h
6
⋅
2
-------------
⎝⎠
⎛⎞
⎠
⎞
+–+–
h
1
x
---
=
2x 1–()e
1
x 1–
-----------
h
1
x
---
=
S
ERIES 2X 1)–(( EXP
1
X 1–
------------
⎝⎠
⎛⎞
X ∞+3
)
,=,⋅
12 6h 12h
2
17h
3
++ +
6 h⋅
-------------------------------------------------------
02 h
3
⋅()+
h
1
x
---
=
hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM