# Complete the square in the denominator make

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Question11. Complete the square in the denominator, make appropriate substitution, and integrate.dxxx10612UMUC Final Exam: Math 141/6382Page
Question12. Find the partial fraction decomposition for the rational function uuand then evaluate the integral duuu)
Question 13. State whether the sequence converges or diverges. If it converges, find its limit.
UMUC Final Exam: Math 141/6382Page
Question14. Using the Integral Testto test the following series for convergence. Solving using other methods or with no detail is not acceptable.32)(ln1nnnf(x)=1x(lnx)231x(lnx)2dx=limn→ ∞31x(lnx)2dx
Question 15. Determine whether the following series converge or diverge. Indicate the test you use.(a) 1sin122kkk1sink ≤10sin2k ≤1k=21+sin2kk1k=21+0k1diverges by comparion test and p-test (p=1)(b) 1232214nnnn
UMUC Final Exam: Math 141/6382Page 10
Question 16. Determine whether the series converges or diverges. If it converges, find its sum
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