HP 40gs User Manual page 207

hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM
Computer Algebra System (CAS)
Typing:
⎛
2
( ⋅ )
SERIES COS 2 X
⎝
gives:
1 8 3
2
〈
-- - --------- - h
– 3h + 2h +
4 3
• 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:
3 5
π π h
h h
⎛ ⎛
-- - ---- - ---- - ------------ -
– h + – + 0
⎝ ⎝
2 3 5
Example 2
Give a 2nd-order expansion of
vicinity of x=+∞, taking as infinitely small
SERIES 2X 1 ) ( ( ⋅
– EXP
gives:
2
12 + 6h + 12h + 17h
------------------------------------------------------ -
6 h ⋅
•
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.
π
⎞
, ,
-- -
X = 4
⎠
6
5
8 h
⎛ ⎞
3 4
π
|
-- - h ---- -
– + 0
⎝ ⎠
-- -
h = X –
3 4
6
1
-- -
h =
.
x
6
⋅
⎞ ⎞
1
⎠ ⎠
-- -
h =
2
x
1
---------- -
x 1 –
( )e
2x 1 –
in the
1
-- -
h =
.
x
1
⎛ ⎞ X
∞
----------- -
, = + , 3)
⎝ ⎠
X 1 –
3
3
( ⋅ )
1
+ 0 2 h
-- -
h =
x
〉
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