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.dxx13/461b. dxx30716,62. Given that rraarararann1)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.6sin3r Be sure to have the correct limits on your integral. Do not evaluate! 65. Use the integration formulaCaxaaxdxxax12222sec to evaluate the integral.2792dxxx76. For the two points with polar coordinates, ),5(1P and ),4/,2(2P 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 .0r4c. Find the rectangular coordinates for each point. 67. Given that ,1limxnnenx find nnnn3lim48. Write the terms 1a thru 5a for each sequence below:a.2103)1(24iiiaaaab. 2sin)1(1nann5,49. State whether the given sequence }{na or series converges or diverges. Give a reason for each answer!a.nn637b. 862631757nnnnnn6c. 13nnnd. 151n6e. 4273354nnnnanf. nan61610.Give an example of a convergent p-series and a divergent geometric series. 4p-series: geometric series:11.Use the integration formulaCaaxxaxdx12sin2 to evaluate the integral .72dxxx Simplify your answer.