HP 40gs User Manual page 208

hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM
14-26
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
+
x = 0 .
Typing:
2 3
(
+
SERIES X ,
X
gives:
1 1 – 1
4 3
----- - h ⋅ ----- - h ⋅ -- - h ⋅
+ +
16 8 2
Example 2
Give a 3rd-order expansion of
–
x = 0 .
Typing:
2 3
(
+
SERIES X , X
X
gives:
1 – 1 – 1 –
4 3
----- - h ⋅ ----- - h ⋅ ----- - h
+ +
16 8 2
Note that h = –x is positive as x → 0
Example 3
If you enter the order as an integer rather than a real, as
in:
2 3
(
+
SERIES X ,
X
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 :
2 3
x + x
in the vicinity of
, )
= 0 3.0
X
2 5
( ) ( )
+ h + 0 h h = x
2 3
x + x
in the vicinity of
– , )
= 0 3.0
2 5
⋅ ( ) ( )
+ + h 0 h h = x –
–
.
0 3 , )
=
X
Computer Algebra System (CAS)