MATH 151 TEST 2 SPRING 2010 4 15 2010 Remember 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 pts 1 Evaluate each of the following or show why they diverge 1 a 4 3 dx 1 6x 6 6 2 Given that a ar ar 2 ar n 1 1 n 1 5 a 3n n 2 3 1 b dx 0 7x a 1 r n evaluate each of the following 1 r b 1 2 1 2 2 1 2 3 1 2 30 7 6 3 Write the repeating decimal 0 7777 as a ratio of integers fraction in lowest terms You must use an infinite series to solve 7 1 2 A 4 Set up an integral that will give the area 2r d of one leaf of the 12 leaf rose r 3 sin 6 Be sure to have the correct limits on your integral Do not evaluate 6 5 Use the integration formula x2 a2 x dx x 2 a 2 a sec 1 C x a to evaluate the integral 9x2 7 dx 2x 7 6 For the two points with polar coordinates P1 5 and P2 2 4 a Plot and label the two points on the same set of axes 4 b Find two other equivalent polar coordinates for P2 at least one of which has r 0 4 c Find the rectangular coordinates for each point 6 n 7 Given that x lim 1 e x n n find n 3 lim n n n 4 8 Write the terms a1 thru a5 for each sequence below a0 4 a a1 2 b i ai 1 3ai 2 n an 1 n 1 sin 2 5 4 9 State whether the given sequence a n or series converges or diverges Give a reason for each answer 7 n 6 3 a 3 c n 1 n n 3 n 6 7n 2 6 n 8 5n 7 n 1 b n n e an 6 1 d 5 n 1 n 4 3n 7 2n 5 n 3 4 f an 6 1 6n 6 10 Give an example of a convergent p series and a divergent geometric series p series 11 Use the integration formula Simplify your answer 4 geometric series x a sin 1 C a 2ax x dx 2 to evaluate the integral 6 7 x x2 dx