MATH 151 TEST 3 SPRING 2010 5 11 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 2 x 1 Compute the Taylor Maclaurin series for f x e 2 1 2 x 3 pts and show that it is the expected series 2 x 2 x 2 3 Be sure to show the formula for the nth derivative and term 10 2 x n f x 2 n e n n n n f 0 2 1 2 2 Find the interval of convergence for the series n 1 n 2 1 3 x 5 6n n2 n 4 11 11 x 1 3 Find the distance between the points 3 7 2 and 8 6 1 35 5 4 If a 3 2 4 2 a b a b 5 1 3 and c 3 5 1 b 2 a b find each of the following 4 7 2 29 13 c Any non zero vector orthogonal to c d 2a 4 5 2 29 1 0 3 5 Compute the 4th degree Taylor polynomial about 1 3 sin cos 6 2 6 2 x 6 for f x sin x Note This is different than the known series about x 0 10 1 3 1 1 2 3 1 3 1 1 4 T 4 x x x x x 2 2 6 2 2 6 2 3 6 2 4 6 6 What is the equation of the sphere centered at the point 4 0 3 with a radius of 5 2 2 2 x 4 y z 3 25 n 1 n 7 What is the maximum possible error if we approximate n 2 4 36 1 n by n 2 n 4 abs val of 37th term 1 37 8 State whether each of the following series is absolutely convergent AC conditionally convergent CC or divergent D Justify your answers n 5 n 1 2 1 n 1 3 2n 3 n n 1 n2 5 n 7 a n 2 2 b n 2 AC ratio test limit c n 2 4n 1 7 9n 27 Div limit 3 0 d 3 1 n n n n 2 n n 4 5 5 n AC geom r 4 9 CC compare to 1 n 1 1 3 x 9 x 2 27 x 3 9 Given that 1 3 x for 3 x 1 and 1 1 2 x 4 x 2 8 x3 1 2 x for 2 x 1 find the 3rd degree Maclaurin polynomial for 1 1 f x 1 3 x 1 2 x by multiplying the two series together 10 2 T 3 x 1 x 7 x 3 x 3 10 Sketch the vector represented by 3 u 2 v 5 6 5