MATH 151 TEST 3 12/13/07 FALL, 2007Remember 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. Calculator answers are not acceptable.Name:____________________________________________________________ pts1. Find the 3rd degree Taylor polynomial for the function xxf 2sin)(  at .8/a Do not use any other known series to do this. Note: 2/1)4/cos()4/sin( . 92. Evaluate each of the following convergent series (note the first series starts at n = 1):a.135nnb. ...2121212121654326,63. Do the following series converge conditionally, converge absolutely, or diverge? Justify.a.nn137b. 11)1(nnn4,5 c. 132)1(nnnn64. Without using another Taylor series, find the (infinite) Taylor series for the function xexf3)(  at .0a Show the terms through 3xand show the general form of the nth term. 95. Find the interval of convergence for the power series 1)43(nnnx. 96. 4,2;1,3 vua. Sketch u and v in standard position (both starting at the origin). Sketch the vector represented by vu using the parallelogram rule. 5b. Find a unit vector in the opposite direction of u. 3c. Find .vu2d. Find a non-zero vector perpendicular to u. 37. If  1,2,1;3,1,2 vu, find each of the following. You may (and should) use any results from a previous part from this question to help with the current part.a.vub. vu2,5c. The angle between u and v (to the nearest hundredth of a radian). 5d. Two different unit vectors that are perpendicular to both u and v. 4 e. Write u as the sum of two vectors, one that is parallel to v and one that is perpendicular to v. 78. If ,1,3,5;4,1,3;2,1,2  cba find the triple scalar product ).( cba69. Give an example (if possible) of a sequence }{na that converges to zero, but the series 1nna diverges.