242test3key014 - Math 242 Section 014 Test#3 N AME Please...

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Unformatted text preview: Math 242 Section 014: Test #3 N AME: ' Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30) There are 6 questions on 6 pages. Points per page: 5, 5, 5, C, 5, 6. The 7th page has some f ormulas you eari refer to if n eeded. [5 p oints] Question 1. D etermine w hether the infinite series is absolutely convergent, conditionally convergent, or divergent. /? +2. boes 'it / ' [5 pointy] Question 2. Find the interval of convergence of t he power seres oo X—^ 1)^ i < - y-2 <3 , 1 -> Z € or [5 p oints] Question 3. Find a power series r epresentation of t he f unction 1 + 2.7; 1 - x- ' Then use the first t hree terms of t hat series ( the constant t erm, the x term. , ? , *, • ^O - . and, the x t erm) t o h ud a n approximation t o 02 1 l 0.999 x fl /.S0 X - / f ^a f -y -f -X 1 + IK + i -0-001 0.0(93 +0.000003 = 1.003003 [6 points] Question 4. Find the first t hree terms of the Taylor series for the function and use those f irst t hree terms to get an approximation for ( 1.04) 1 / 2 . 60 = 1 X -f- 0.02 - 0.0002. ' i.om [5 points] Question 5. Find the first three terms of the Taylor series for t he function f ( x ) = c~x sin.x. -2L f *! _:*! + . . . |> -^ -?' * 3! >™ ^ 3) - l_^ - 5! . V- - - '7! 3! 3. 5 . i-x 1' I-'X z~ * 'Y A ^ L /v A 3 A/3 — ^/v3 — X -if" ^^ 3 O^ - /X - [6 p oints] Question 6. Consider the p arametric curve :/; — t + lnt, y ~ t — hit, where 0 < t < oo. F ind dy/dx and d2y/dx'2. Find w here the curve is increasing, decreasing, concave up. or concave down. Sketch t he c urve. i + 1 - J=1 -b <L <! dt -t +1 ,,i 1 up ...
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This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.

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242test3key014 - Math 242 Section 014 Test#3 N AME Please...

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