242test3key050

# 242test3key050 - M ath 242 Section 050 Test#3 NAME „...

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Unformatted text preview: M ath 242 Section 050: Test #3 NAME: „ _____ There are 6 questions on 6 pages. P ointy per page: 5, 5, 5, 0, 5, 6. The 7th page has some f ormulas you can refer to if needed. [5 points] Question 1. D etermine whether the i nfinite series is absolutely convergent, conditionally convergent, or divergent. - \.<l Tf J-t - "- I/O [5 points] Question 2. F ind t he interval of convergence of t he power ^ ' 3??, an = - as 9 < 5" -? or < [5 p ointy] Question 3. Find a power series r epresentation of the f unction l+4xl-x' Then use the f irst t hree terms of t hai, series (the constant term, the x t erm, ,, 9 r! 1 -004 and the x t erm to imd an a pproximation to ---. ; 0.999 /)lso l-'X 0(^0.001 ^ 1 +0.00^ ^ i± 0.005 +0.000005 L'°'ooi ~ [6 points] Question 4. Find the first t hree t erms of t he Taylor series for t he function /(*) = ( !+a:) 1 / 2 and use those first three terms to get an approximation for (1.08)1/2. o " ^ ' i -L+. 2. [5 points] Question 5. Find t he f irst t hree terms of the Taylor series for the function f ( x ) =e. x sin(-x). 11 3! 2\L 5. 7 35" 3 *_ -Y *3 (o - ^y^ 3 z — s [6 points] Question 6. Consider the p arametric curve x — t + \u t, y — t — ln /,, whore 0 < t < oo. F ind dy/dx jiiid d2y/dx2. F ind where the curve is increasing, decreasing, concave up, or concave down. Sketch the curve. / •t /)< ;f i<l d d -t-fl A\WMjS C\$f\cd\fc uf> ...
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242test3key050 - M ath 242 Section 050 Test#3 NAME „...

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