hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM

 

1

h

4

–1

h

3

1

⋅ h

2

+ h + 0(h

5

)

 

(h = x)

 

 

 

----- ⋅

 

+ ----- ⋅

 

+ --

 

 

 

 

 

16

 

 

8

 

 

2

 

 

 

 

 

 

 

 

 

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(3X2-8X-11)

 

 

 

 

 

 

 

 

gives, in step-by-step mode:

 

 

 

 

 

 

 

F = (3 ⋅ x2 – 8 ⋅ x – 11)

 

 

 

 

 

 

 

 

F' = (3 ⋅ 2 ⋅ x – 8)

 

 

 

 

 

 

 

 

 

 

→ (2 ⋅ (3 ⋅ x–4))

 

 

 

 

 

 

 

 

 

 

Variation table:

 

 

 

 

 

 

 

 

–∞

–

4

 

 

+

 

+∞

X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

--

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

+∞

↓

–49

 

 

↑

 

+∞

F

 

 

 

 

 

 

 

---------

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 [–∞,

4

], reaching a minimum of

–49

--

---------

at x =

4

 

3

 

4

 

3

. It then increases in the interval [

, + ], reaching

3

3

 

--

 

 

 

--

∞

 

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).

Computer Algebra System (CAS)

14-27