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whiskey0905

# whiskey0905 - 04 1 2 4[5 points Question 5 Find the ﬁrst...

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Math 242 Section 014: Test #3 NAME: 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, 6, 5, 6. The 7th page has some formulas you can refer to if needed. [5 points] Question 1. Determine whether the inﬁnite series X n =0 ( - 1) n n n 4 + 2 is absolutely convergent, conditionally convergent, or divergent. 1

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[5 points] Question 2. Find the interval of convergence of the power series X n =0 ( - 1) n ( x - 2) n 3 n + 1 . 2
[5 points] Question 3. Find a power series representation of the function 1 + 2 x 1 - x . Then use the ﬁrst three terms of that series (the constant term, the x term, and the x 2 term) to ﬁnd an approximation to 1 . 002 0 . 999 . 3

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[6 points] Question 4. Find the ﬁrst three terms of the Taylor series for the function f ( x ) = (1 + x ) 1 / 2 and use those ﬁrst three terms to get an approximation for (1

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Unformatted text preview: . 04) 1 / 2 . 4 [5 points] Question 5. Find the ﬁrst three terms of the Taylor series for the function f ( x ) = e-x sin x. 5 [6 points] Question 6. Consider the parametric curve x = t +ln t , y = t-ln t , where 0 < t < ∞ . Find dy/dx and d 2 y/dx 2 . Find where the curve is increasing, decreasing, concave up, or concave down. Sketch the curve. 6 If helpful, you may use any of these formulas in any of the test questions. sin 2 x = 1 2 ± 1-cos 2 x ² cos 2 x = 1 2 ± 1 + cos 2 x ² Z 1 1 + x 2 dx = ? Z sec x dx = ln | sec x + tan x | + C 1 + x 1! + x 2 2! + x 3 3! + ··· = ? x-x 3 3! + x 5 5!-x 7 7! + ··· = ? 1-x 2 2! + x 4 4!-x 6 6! + ··· = ? x-x 2 2 + x 3 3-x 4 4 + ··· = ? 7...
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whiskey0905 - 04 1 2 4[5 points Question 5 Find the ﬁrst...

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