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Please sign (or type) your name below the following honor pledge: I have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz.Name:________Date: ___4/26/2018____QUIZ # 7 ProblemsMath 141/7982, Due April 29, 2018 (10 questions, 10 points each)1.Determine whether or not the alternating series converge or diverge.∑n=1∞(−1)nln(n2+1)❑
2.Test the series for absolute convergence.∑n=1∞(−1)nn33n3.Test the convergence of the series using Root or Ratio Tests.∑n=1∞(2n+33n+2)n
4.Test the convergence of the series using Root or Ratio Tests.∑n=1∞(ln(n)n)nWork:5.Find the interval of convergence for the power series∑n=1∞(x−3n)nSolution: -∞ ≤ ∞ ≤ ∞Work:
6.Find the interval of convergence for the power series∑n=1∞12n+1xn+1Solution: By the ratio test the given interval converges Work:7.Use the substitution method and a known power series to find power series for the following function (use one Sigma notation):f(x)=sin(3x)xSolution: Work:
8.Calculate the Maclaurin series to the x3term:f(x)=12+xSolution: f(x)= (1/2) – (1/4)x + (1/8)x^2 – (1/16)x^3Work:9.Evaluate (use Maclaurin series for exlimx→ex−1−xx2)Solution: (1/2)Work:
10.How many terms of the Maclaurin series for sin(x)are needed to approximate the values off(x)=sin(x)on the interval [−π2,π2]with an error less than 10−10Solution: Work: