MATH 141 Quiz 6 - Please sign(or type your name below the following honor pledge I have completed this quiz by myself working independently and not

# MATH 141 Quiz 6 - Please sign(or type your name below...

• Test Prep
• 6
• 100% (6) 6 out of 6 people found this document helpful

This preview shows page 1 - 6 out of 6 pages.

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 Problems Math 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)nn33n 3.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)n Work: 5.Find the interval of convergence for the power seriesn=1(x3n)n Solution: -∞ ≤ ∞ ≤ ∞Work:
6.Find the interval of convergence for the power seriesn=112n+1xn+1 Solution: 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)x Solution: Work:
8.Calculate the Maclaurin series to the x3term:f(x)=12+x Solution: f(x)= (1/2) – (1/4)x + (1/8)x^2 – (1/16)x^3 Work: 9.Evaluate (use Maclaurin series for exlimx→ex1xx2 ) 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 10 Solution: Work: