MATH 152 FALL 2010 COMMON EXAM II VERSION A LAST NAME First name print INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 10 mark the correct choice on your ScanTron using a No 2 pencil For your own records also record your choices on your exam as Scantrons will NOT be returned 3 In Part 2 Problems 11 15 present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Be sure to write your name section and version letter of the exam on the ScanTron form THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature 1 1 The sequence an 1 4 b converges to 5 1 c converges to 5 d diverges 2 a converges to e converges to 0 The sequence an a 1 5 e n 1 n 2n2 2 3n2 1 diverges 2 3 2 c converges to 3 d converges to 2 3 b converges to e converges to 0 Which of the following is the form of the partial fraction decomposition of a b c d e A B C x 1 x 1 2 x2 2x 3 Ax B C D x 1 2 x 3 x 1 A B C D E 2 x 3 x 1 x 1 x 1 x 3 A B Cx D 2 2 x 1 x 1 x 2x 3 A Bx C D 2 2 x 1 x 1 x 2x 3 2 x x 3 2x 3 1 2 x2 4 The nth partial sum of a series following statements is true I The series X II The series X an is given by sn n 1 2n 1 Which of the n 1 an converges to 2 n 1 X an diverges by the Test for Divergence n 1 III The sequence an converges to 0 only I and III are true b only I is true c only II and III are true a only II is true e all three statements are true d 5 Which of the following integrals gives the area of the surface obtained by rotating the curve y e2x 0 x 1 about the x axis 1 a 2 x 1 4e4x dx 0 1 b 2 e2x 1 4e4x dx 0 r 1 1 c 2 x 1 e4x dx 4 0 1 d 2 1 2e2x dx 0 r 1 1 2x e 2 e 1 e4x dx 4 0 3 6 After an appropriate substitution the integral 2 3 4 x2 dx is equivalent to which of the following 2 a 4 sec tan2 d 6 b 2 2 4 2 2 2 2 cos d 3 c cos2 d 6 d tan d 6 e 4 cos2 d 3 7 Compute 3 1 1 dx x2 4 3 b The integral diverges a ln 9 4 d 3 2 e 3 c 8 Which statement is true about the integral sin2 x dx x2 1 dx x 1 a The integral diverges by oscillation b The integral converges to 0 c d The integral diverges by comparison to The integral diverges by comparison to 1 12 dx 1 e The integral converges by comparison to 1 4 1 dx x2 9 Which statement is true about the series X n 2 n3 n 5 X 1 1 n and is divergent a The series is divergent because 3 n 5 n n n 2 b c d e 10 X 1 1 n 2 and is convergent The series is convergent because 3 n 5 n n2 n 2 n The series is convergent because lim 3 0 n n 5 n 6 0 The series is divergent because lim 3 n n 5 n X 1 3 The series is convergent because lim n 1 5 1 and is convergent 2 n n 2 n n 2 Which of the following series is convergent X 1 a n n 1 X 1 b 3 2 n n 1 c d X n 2 X n 1 e 1 n ln n 1 3 n More than one of these series is convergent 5 PART II WORK OUT Directions Present your solutions in the space provided Show all your work neatly and concisely and Box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 11 10 points Compute dx x2 x2 4 6 12 8 points each Find the sum of the following series or show they are divergent a X 2 2n n 0 b X n 0 10n 2 n 1 n 3 7 13 6 points each Given the curve parametrized by x cos t t sin t y sin t t cos t 0 t 2 a Find the length of the curve b SET UP BUT DO NOT EVALUATE an integral to find the area of the surface formed by rotating the curve about the y axis 8 14 10 points Compute 3x2 4x 11 dx x 1 x2 4 9 15 6 points each Given the series X 3 3n2 e n n 1 a Use the Integral Test to show that the series is convergent b According to Matlab the third partial sum s3 1 107663875 Use the remainder theorem to estimate the largest possible error 10 DO NOT WRITE BELOW Question Points Awarded Points 1 10 40 11 10 12 16 13 12 14 10 15 12 TOTAL 100 11
View Full Document
Unlocking...