MATH 151 TEST 2 FALL, 2010 11/10/2010Remember 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. Integrate each of the following:a.6 x +1x2+4−12(x+4)3(¿)dx∫¿ b. ∫−∞06 e3 xdx 12,6 c. ∫02dx7(2−x) d. ∫2 x−1(x+3)(x−2)dx5,82. Use the integral tables on the back of page 3 to evaluate (tell which number you used):a.∫dx3 x√7 x+4 b. ∫7 x(2 x+5)2dx6,63. Find the partial fraction (find the coefficients!) expansion of:x2−3 x +1x2(x+2)104. Tell what each sequence or series converges to, or explain why it diverges:a.∑n=2∞[(−1)n+ 1(10)(23)n] b. ∑n=7∞[−5n3 / 4]12c. {ecos(1n)} d. ∑n=5∞[n3−2 n+14+n2−2 n3]85. Find two different sets of polar coordinates for the point with rectangular coordinates (4, 3). Make one of your points have a negative r. Use your calculator to approximate θ to thenearest thousandth of a radian.76. Find an equivalent equation in x-y coordinates for the polar equation 7=r sin θ+r2cos2θ. Sketch the graph (this should not need a calculator at all!) . 77. Give a specific example of each of the following (or show why it is impossible):a. A convergent sequence {an} whose associated series ∑n=1∞(an) diverges. 4b. A convergent series ∑n=1∞(an) whose associated sequence {an} diverges. 48. Write the first five terms of the sequence, a1 through a5:5 a1=2 ak={−3 ak −1if k is evenak−2+ak−1if k is