practice_problems midterm 2

Practice_problems - PRACTICE PROBLEMS(MATH 31B MIDTERM 2 Problem 1 Compute the integral 2x4 4x2 x 1 dx(x2 1)2(x − 1 Problem 2 Compute the

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Unformatted text preview: PRACTICE PROBLEMS (MATH 31B, MIDTERM 2) Problem 1. Compute the integral 2x4 + 4x2 + x + 1 dx. (x2 + 1)2 (x − 1) Problem 2. Compute the integral 4x2 − 3x + 2 dx. 4x2 − 4x + 2 Problem 3. Compute the integral 3 1 dx √ . x−2 Problem 4. Does the integral ∞ 0 x2 e−x dx converge? 1 x2 dx √ . 0 1−x2 Problem 5. Compute the integral Problem 6. Find the length of the curve y = ex + e−x , where x ∈ [0, 1]. Problem 7. Let a1 = 1 , a2 = 0 and an+1 = 1 (sin an + sin an−1 ). Assuming that 2 the limit exists, find it. Problem 8. Determine if the sequence converges. (You need to justify your answer). If it converges, find its limit: (1) an = (2) an = 1 (3) a1 = c, where c is a given positive number; an+1 = 2 (an + (4) an = (2n) nn (n+1)n . 2n ln n2 ln(3n2 ) . cos4 n 2n . c an ). Problem 9. Does the series converge or diverge? If converges, find its limit. (1) (2) (3) (4) (5) (6) ∞ n=1 ∞ n=1 ∞ n=1 ∞ n=1 ∞ n=2 ∞ n=1 1 n(n+1) ; 2 √; 3n 2n 2n +3n 2n 3n ; cos(1/n); 1 n log n ; n2 2n . 1 ...
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This note was uploaded on 10/13/2008 for the course MATH 31B taught by Professor Valdimarsson during the Winter '08 term at UCLA.

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