116pexam03 - t with y(0 = 0 and y(0 =-2 6 Identify and...

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Practice Exam #3 1. Determine convergence or divergence for the following series. Be sure to state your reasoning. (a) X n =1 ln n n 2 (b) X n =1 (sin n ) 2 4 n +1 (c) X n =1 n 3 n + 1 n (d) X n =2 1 n 3 + n 2. Find the interval of convergence for X n =0 ( x - 17) n 4 n (3 n + 2) . 3. Use power series to evaluate Z tan - 1 (3 x 2 ) dx. 4. Use power series to solve the differential equation y 00 - 4 y 0 + 3 y = 0 . If you choose not to find a pattern, provide at least five nonzero terms. Now use Laplace transforms if y (0) = 0 and y 0 (0) = - 2. 5. Use Laplace transforms to solve the differential equation y 00 - 4 y 0 + 3 y = 4
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Unformatted text preview: t with y (0) = 0 and y (0) =-2. 6. Identify and graph the conic section-( x-3) 2 9 + ( y + 1) 2 16 = 1 . 7. Find the length traveled by the parametric curve x ( t ) = t 2 + 1 y ( t ) = t 2-3 for 0 ≤ t ≤ 6. 8. Find the length swept out along one petal of r = sin (3 θ ). 9. Solve the diferential equation y 00 + 3 y + 2 y = 0 iF y (0) = 1 and y (0) = 0. 10. Solve the diferential equation y 00 + 2 y + y = 4 e-t iF y (0) = 2 and y (0) =-1....
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