HP 40gs, Руководство пользователя

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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.
SERIES COS 2 X
⋅ ( )
2
X
π
6
---
= 4
, ,
⎝ ⎠
⎛ ⎞
1
4
---
3 h 2 h
2
8 3
3
----------
h
3
8
3
---
h
4
0
h
5
4
-----
⎝ ⎠
⎛ ⎞
+ – + + –
h X
π
6
---
– =
〈 | 〉
h
1
x
---
=
π
2
---
⎝
⎛
h
h
3
3
-----
h
5
5
----- 0
π
h
6
⋅
2
-------------
⎝ ⎠
⎛ ⎞
⎠
⎞
+ – + –
h
1
x
---
=
2 x 1 –
( )
e
1
x 1 –
-----------
h
1
x
---
=
SERIES 2 X 1
)
–
( (
EXP
1
X 1 –
------------
⎝ ⎠
⎛ ⎞
X
∞
+ 3) , = ,
⋅
12 6 h 12 h
2
17 h
3
+ + +
6 h
⋅
------------------------------------------------------- 0 2
h
3
⋅ ( )
+
h
1
x
---
=
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