MATH 151 TEST 2 SPRING, 2010 4/15/2010Remember to keep your work neat and orderly. Show all of your work. NO WORK = NO CREDIT! Read each question carefully and be sure to answer the question that was asked. Good luck!Name:____________________________________________________________ pts1. Evaluate each of the following or show why they diverge:a.dxx13/461b. dxx30716,62. Given that rraarararann1)1(...12, evaluate each of the following:a.2135)1(nnnb. 3032)2.1(...)2.1()2.1(2.1 7,63. Write the repeating decimal ...7777.0 as a ratio of integers (fraction in lowest terms). You must use an infinite series to solve! 74. Set up an integral that will give the area (drA221) of one leaf of the 12-leaf rose.6sin3r Be sure to have the correct limits on your integral. Do not evaluate! 65. Use the integration formulaCaxaaxdxxax12222sec to evaluate the integral.2792dxxx76. For the two points with polar coordinates, ),5(1P and ),4/,2(2P a. Plot and label the two points on the same set of axes. 4b. Find two other equivalent polar coordinates for 2P, at least one of which has .0r4c. Find the rectangular coordinates for each point. 67. Given that ,1limxnnenx find nnnn3lim48. Write the terms 1a thru 5a for each sequence below:a.2103)1(24iiiaaaab. 2sin)1(1nann5,49. State whether the given sequence }{na or series converges or diverges. Give a reason for each answer!a.nn637b. 862631757nnnnnn6c. 13nnnd. 151n6e. 4273354nnnnanf. nan61610.Give an example of a convergent p-series and a divergent geometric series. 4p-series: geometric series:11.Use the integration formulaCaaxxaxdx12sin2 to evaluate the integral .72dxxx Simplify your answer.
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