victor1325 - y = ln(cos x ) between x = 0 and x = / 3. 3 [5...

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Math 242 Section 012: Test #2 NAME: Please 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, 5, 6, 6. Show your work. A correct answer with little or no reasoning may receive a low score. (However, there is no need to be wordy.) The 7th page has some formulas you can refer to if needed. [5 points] Question 1. Determine whether the improper integral Z 0 x ( x 2 + 3) 2 dx converges or diverges. If it converges, find its value. 1
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[5 points] Question 2. Using an intelligent first approximation, use one iteration of Newton’s method to get a very good approximation to 10002. 2
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[5 points] Question 3. Find the length of the curve
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Unformatted text preview: y = ln(cos x ) between x = 0 and x = / 3. 3 [5 points] Question 4. Determine whether the series X n =1 1 + 2 n 4 n converges, and if it converges, nd its sum. 4 [6 points] Question 5. Determine whether the series X n =2 1 n (ln n ) 4 / 3 converges or diverges. (Provide a reason.) 5 [6 points] Question 6. Determine whether the series X n =1 1 n sin 1 n converges or diverges. (Provide a reason.) 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 cos 2 x = 1 2 1 + cos 2 x Z 1 1 + x 2 dx = ? Z sec x dx = ln | sec x + tan x | + C 7...
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victor1325 - y = ln(cos x ) between x = 0 and x = / 3. 3 [5...

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