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242test3key012

# 242test3key012 - 1 3 x/3 o f 1 i ~>"7 ^ L ^ i J-2 3...

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NAME: Math 242 Section 012: Test #3 KEY Ploa.sc circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30) There are 6 questions on 6 pages. Points per page: 5, 5, 5, 0, 5, 6. The 7tli page has some formulas you can refer to if needed. [5 points] Question 1. Determine whether the infinite series is absolutely convergent, conditionally convergent, or divergent. n ae\$. <V5 ' CffnMWK a i o r M , H - i lAJ£

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[5 points] Question 2. Find the interval of convergence of the power series In + 1 -3 2 n v"» n . , ' 2
S [5 points] Question 3. Find a power scries representation of the function 1 + 3x 1 -x ' Then use the first three terms of that series (the constant term, the x term, 7 ,. , 1-003 and the x term) to find au approximation to L . 1-y o = 0.001 0.003 0.999 -/-'x 4- I +0.00^ +aocooo<t

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[6 points] Question 4. Find the first three terms of the Taylor series for the function and use those first, three terms to get an approximation for (LOG)

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Unformatted text preview: 1 / 3 . x '/3 o f 1! i + ' ~> "7 , /-, ^ L ^ i J---2 3 0,02 1 [5 points] Question 5. Find the first three terms of the Taylor series for the function f(x) = er :i; cosx. P ~--± 1-* 4-. . V i i ' _ _ _ _ _ ~ ' I 1 o!-1-*-cos *-.1-4-A/ X-Z 1 \ ± V i * / *. f2L_^. .Y/-*-^-*_•». 1.' 2! 3.' X 2.' ^.' *.' 1 2- "2-/K,-y 4. ^-O-2" ^ 'T) \)<l SSifa Id' 5 fi^ OA£ h/voA?-f-g/^ '-" ^ — o<" __ 2L. = IT c, pfsf-f/lff^ ^f^S • y i 'V 3 [6 points] Question 6. Consider the parametric curve x = t-\-\\\ y — i —In t, where 0 < t < oo. Find dy/dx and d' 2 y/dx 2 . Find where tlie curve is increasing, decreasing, concave up, or concave down. Sketch the curve. dt t-1 i ~~ , _!-k 1 /), ,f ,f-t +1 AllXJWS CW\CAW up...
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242test3key012 - 1 3 x/3 o f 1 i ~>"7 ^ L ^ i J-2 3...

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