hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM

You must be in Rigorous (not Sloppy) mode to apply SERIES with unidirectional expansion. (See “CAS modes” on page 14-5 for instructions on setting and changing modes.

Example 1

Give a 3rd-order expansion of x2 + x3 in the vicinity of x = 0+.

Typing:

SERIES(X2 + X3, X = 0, 3.0)

gives:

 

 

 

 

 

 

 

 

 

 

 

 

 

1

⋅ h

4

–1

⋅ h

3

1

⋅ h

2

+ h + 0(h

5

)

 

(h = x)

 

-----

 

+ -----

 

+ --

 

 

 

16

 

 

8

 

 

2

 

 

 

 

 

 

 

Example 2

Give a 3rd-order expansion of x2 + x3 x = 0–.

Typing:

SERIES(X2 + X3, X = 0, –3.0)

gives:

 

 

 

 

 

 

 

 

 

 

 

 

 

–1

⋅ h

4

+

–1

⋅ h

3

+

–1

⋅ h

2

+ h + 0(h

5

)

-----

 

-----8

 

-----2

 

 

16

 

 

 

 

 

 

 

 

 

 

 

Note that h = –xis positive as x → 0–.

in the vicinity of

(h = –x)

Example 3

If you enter the order as an integer rather than a real, as in:

SERIES(X2 + X3, X = 0, 3)

you will get the following error:

SERIES Error: Unable to find sign.

Note that if you had been in Sloppy rather than Rigorous mode, all three examples above would have returned the

same answer as you got when exploring in the vicinity of x = 0+:

14-26

 

 

Computer Algebra System (CAS)