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 3 1 6 x 4 3 dx 71x dx a 1 b 0 6 6 div 2 2 Given that a a ar ar ar n 1 n 1 n a 1 r 1 r evaluate each of the following 1 5 3n n 2 7 6 b 5 12 2 3 30 1 2 1 2 1 2 1 2 1418 26 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 7 9 1 A r 2 d 2 4 Set up an integral that will give the area 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 6 92 sin 2 6 d 0 5 Use the integration formula x 2 a 2 x dx x 2 a2 a sec 1 C x a to evaluate the integral 2 9x 7 dx 2x 7 3 2 7 7 9 x 2 sec 1 x C 9 9 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 2 2 4 2 34 c Find the rectangular coordinates for each point P1 5 0 P 2 2 2 2 2 x n x n 3 lim 1 e lim n 7 Given that n find n n n 4 3 e 8 Write the terms a1 thru a5 for each sequence below 6 a0 4 a1 2 i ai 1 3 ai 2 a an 1 n 1 sin b n 2 5 4 2 12 6 36 18 1 0 1 0 1 9 State whether the given sequence an or series converges or diverges Give a reason for each answer a n 6 7 3 n Div geom with r 1 b n 8 c n 1 n n 6 div limit of nth term not 0 4 an f conv to 0 1 6n conv to 0 10 Give an example of a convergent p series and a divergent geometric series p series n12 n 1 6 1 n 1 div p series p 2 3 1 e 6 2 5 d n 3 n 7 an 5 3 2 n n 4 6 div limit of nth term not 0 3 3 n n 7 n 5 n 6 7 n 1 geometric series 53 n 1 n 4 11 Use the integration formula 7 x x 2 dx 2ax x 2 sin 1 x aa C to evaluate the integral dx Simplify your answer 7 sin 1 2 x 1 C 2 6