HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 209
Tabvar, Taylor0
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hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM TABVAR TAYLOR0 --1--- ⋅ h4 + -----1- ⋅ h3 + 1-- ⋅ h2 + h + 0(h5) (h = x) 16 8 2 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 4---9- ↑ +∞ 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 ------4---9- at x = 4-- . It then 3 increases in the interval [ 4-- , +∞], 3 reaching 3 3 a maximum of +∞. Note that "?" appearing in the variation table indicates that the function is not defined in the corresponding interval. 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