HP 40gs, User Manual

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Computer Algebra System (CAS) 14-27
TABVAR
Variation table
TABVAR has as a parameter an expression with a
rational derivative.
TABVAR returns the variation table for the expression in
terms of the current variable.
Typing:
TABVAR(3X
2
-8X-11)
gives, in step-by-step mode:
Variation table:
The arrows indicate whether the function is increasing or
decreasing during the specified interval. This particular
variation table indicates that the function F(
x ) decreases
for x in the interval [–
∞
, ], reaching a minimum of
at x = . It then increases in the interval [ , +
∞
], reaching
a maximum of +
∞
.
Note that “?” appearing in the variation table indicates
that the function is not defined in the corresponding
interval.
TAYLOR0 Limited expansion in the vicinity of 0
TAYLOR0 has a single argument: the function of x to
expand. It returns the function’s limited 4th-relative-order
expansion in the vicinity of x=0 (if x is the current
variable).
1
16
------
h
4
⋅
1 –
8
------
h
3
⋅
1
2
---
h
2
⋅
h + + + 0 h
5
( )
+ h x =
( )
–
∞
–
+ +
∞
X
+
∞
↓ ↑
+
∞
F
F 3 x
2
⋅
8 x
⋅
– 11 –
( )
=
F ' 3 2 x 8 –
⋅ ⋅ ( )
=
2 3 x 4 –
⋅ ( ) ⋅ ( ) →
4
3
---
49
–
3
----------
4
3
---
49
–
3
----------
4
3
---
4
3
---
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