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practice_problems midterm 2

# practice_problems midterm 2 - PRACTICE PROBLEMS(MATH 31B...

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PRACTICE PROBLEMS (MATH 31B, MIDTERM 2) Problem 1. Compute the integral integraldisplay 2 x 4 + 4 x 2 + x + 1 ( x 2 + 1) 2 ( x - 1) dx. Problem 2. Compute the integral integraldisplay 4 x 2 - 3 x + 2 4 x 2 - 4 x + 2 dx. Problem 3. Compute the integral integraldisplay 3 1 dx x - 2 . Problem 4. Does the integral integraltext 0 x 2 e - x dx converge? Problem 5. Compute the integral integraltext 1 0 x 2 dx 1 - x 2 . Problem 6. Find the length of the curve y = e x + e - x , where x [0 , 1] . Problem 7. Let a 1 = 1 , a 2 = 0 and a n +1 = 1 2 (sin a n + sin a n - 1 ) . Assuming that the limit exists, find it. Problem 8. Determine if the sequence converges. (You need to justify your an- swer). If it converges, find its limit:
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