Student Print Section Last First Middle Student Sign Student ID Instructor MATH 152 Exam 3 Fall 2000 Test Form B 1 9 45 10 10 11 15 Part II is work out Show all your work Partial credit will be given 12 10 You may not use a calculator 13 10 14 10 Part I is multiple choice There is no partial credit TOTAL 1 Part I Multiple Choice 5 points each There is no partial credit You may not use a calculator 1 The series n 1 a b c d 1 n n is absolutely convergent convergent but not absolutely convergent divergent none of the above 2 Determine the interval of convergence of the power series a b c d e n 0 2 4 2 4 4 2 4 2 3 Compute a b c d 25 3 125 3 125 2 75 2 x 3 n n 1 3 n 5 2 n n 0 e 2 4 Find the 3 rd degree Taylor polynomial for f x e 2x about x 1 a e 2 2e 2 b e 2 2e 2 c e 2 2e 2 d e 2 2e 2 e e 2 2e 2 x 1 x 1 x 1 x 1 x 1 5 Compute a 4 b 2 n 0 n 1 2 2e 2 2e 2 4e 2 4e 2 4e 2 n 1 x 1 x 1 x 1 x 1 x 1 2 2 2 2 2 4 e 2 x 1 3 3 4 e 2 x 1 3 3 8e 2 x 1 3 8e 2 x 1 3 8e 2 x 1 3 HINT Differentiate xn n 0 c 4 9 2 d e 4 6 Find the Maclaurin series for f x sin 2x a b c d e 3 3 5 5 2x 2 x 2 x 3 5 3 5 2x 2x 2x 3 5 3 5 7 x x x x 3 5 7 3 5 7 x x x x 3 5 7 3 5 2x 2x 2x 3 5 7 7 2 x 7 2x 7 7 C C C C 2x 7 7 C 3 7 Find the equation of the circle for which one diameter has endpoints P 1 1 a b c d e x 3 x 3 x 4 x 3 x 4 2 2 2 2 2 y 4 y 4 y 5 y 4 y 5 2 2 2 2 2 25 5 25 5 25 8 Consider the triangle with vertices A 0 0 0 B 1 1 0 a b c d e and Q 7 9 and C 0 2 2 Find the angle at A 0 30 45 60 90 9 Find a unit vector which is orthogonal to the plane containing the points P 1 0 0 Q 0 2 0 and R 0 0 3 6 3 2 a 11 11 11 b 6 3 2 c 6 3 2 6 3 2 d 7 7 7 6 3 2 e 7 7 7 4 Part II Work Out Show all your work Partial credit will be given You may not use a calculator 10 10 points Determine if each of the following series converges or diverges Say why Be sure to name or quote the test s you use and check out all requirements of the test If it converges find the sum If it diverges does it diverge to or neither a n 1 n 1 n n n 1 Circle one Converges Diverges Circle one Converges Diverges Explain b n 1 1 1 3n Explain 5 11 15 points Determine if each of the following series converges or diverges Say why Be sure to name or quote the test s you use and check out all requirements of the test n 3 a n n 0 Circle one Converges Diverges Circle one Converges Diverges Circle one Converges Diverges Explain 1n 4 5 b n 1 n 1 n 1 2 n Explain n ln1n c n 2 n 2 Explain 6 12 10 points a Find the power series representation for f x convergence 1 1 x2 centered at x 0 and its radius of b Find the power series representation for f x x tan 1 x centered at x 0 and its radius of convergence HINT tan 1 x x 0 1 1 t2 dt 7 13 10 points Determine the interval of convergence of the power series n 1 x 2 n Be sure to n 1 3 3 n show how you checked the convergence at the endpoints 14 10 points Find the volume of the parallelepiped with adjacent edges PQ PR and PS where P 1 1 1 Q 2 3 1 R 4 1 5 and S 1 3 4 8
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