HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 207

hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM Typing: S E R I E S ⎝⎛ C O S ( 2 ⋅ X)2, X = π-- , 6 4⎠⎞ gives: 〈1-4 - 3h + 2h2 + 8--------3- h3 3 - 8-- h4 3 + 0⎝⎛h--4--5⎠⎞ |h = X - π-- 〉 6 • Example - Expansion in the vicinity of x=+∞ or x=-∞ Example 1 Give a 5th-order expansion of arctan(x) in the vicinity of x=+∞, taking as infinitely small h = 1-- . x Typing: SERIES(ATAN(X),X =+∞,5) gives: ⎛ ⎝ π-2 - h+ h----3 3 - h----5 5 + 0 ⎛ ⎝ -π----⋅-2--h----6⎠⎞ ⎞ ⎠ h = 1-x Example 2 -----1------ Give a 2nd-order expansion of (2x - 1)ex - 1 in the vicinity of x=+∞, taking as infinitely small h = 1-- . x SERIES((2X - 1 ) ⋅ EXP⎝⎛X-----1------1--⎠⎞ , X = + ∞, 3) gives: 1---2-----+-----6---h-----+--6---1-⋅--2-h--h---2----+-----1---7---h----3 + 0(2 ⋅ h3) h = 1-x • Unidirectional expansion To perform an expansion in the vicinity of x = a where x > a, use a positive real (such as 4.0) for the order. To perform an expansion in the vicinity of x = a where x < a, use a negative real (such as -4.0) for the order. Computer Algebra System (CAS) 14-25