MATH 152 Fall 2022 COMMON EXAM II VERSION B FIRST NAME print LAST NAME print INSTRUCTOR UIN SECTION NUMBER 1 The use of a calculator laptop or computer is prohibited 2 TURN OFF cell phones and put them away If a cell phone is seen during the exam your exam will be collected and you will receive a zero 3 In Part 1 mark the correct choice on your ScanTron using a No 2 pencil The scantrons will not be returned therefore for your own records also record your choices on your exam 4 In Part 2 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 THE AGGIE CODE OF HONOR 5 Be sure to fill in your name UIN section number and version letter of the exam on the ScanTron form DIRECTIONS An Aggie does not lie cheat or steal or tolerate those who do Signature 22 Some integrals that may or may not be useful sec3 x dx 1 sec x tan x 1 ln sec x tan x C YMLNWK csc3 x dx 1 csc x cot x 1 ln csc x cot x C 2 2 1 This page left intentionally blank 2 PART I Multiple Choice 3 5 points each 1 nn2 2n2 5 1 The sequence an a Diverges 1 b Converges to2 c None of these d Converges to 0 e Converges to 1 2 2 Which of the following is an appropriate substitution to use when solving the integral 16x2 9 dx 3 tan 43sin 44sec 34sin 33sec 4 a x b x c x d x e x 3 Which of the following is a proper Partial Fraction Decomposition for the rational function 5x 1 x 3 x2 4x 3 x2 4 Bx C Dx E x2 4x 3 a x 3 x2 4 Bx C D Ex F b x 3 x 3 2 x 1 x2 4 Dx E c x 3 x 3 2 x 1 x2 4 d x 3 x 3 2 x 1 x 2 x 2 D D C C B B A A A A 3 e None of these 4 1 for all positive n Determine if n a1 4 10 an 1 7 a 4 Assume that the sequence an is decreasing and bounded below by 1 i e an the sequence is convergent or divergent and a Convergent to 2 b Convergent to 1 c Divergent 10 d Convergent to7 e Convergent to 5 5 After an appropriate substitution the integral a 81 sin2 cos2 d b 81 sec3 tan2 d c 27 sec2 tan d d 9 cos2 d e 27 sin2 cos d x2 9 x2 dx is equivalent to which of the following e1 i e1 i 1 i 1 6 The series a converges to 0 b None of these c converges to e 1 d diverges e converges to e 5 0 n3 n 1 4 value Using The Remainder Estimate for the Integral Test determine the smallest of n that ensures 7 Let s 1 1 that Rn s sn 44 a n 7 b n 8 c n 6 d n 5 e n 4 x 2 x2 4 dx 8 Compute a ln 20 ln 4 1 b ln 20 ln 4 arctan 2 2 c ln 6 ln 2 1 ln 20 ln 4 2 d arctan 4 2 e ln 20 ln 4 2 arctan 4 be a series whose nth partial sum is 9 Let 2 a a4 3 b None of these 1 c a4 211 d a4 15 e a4 1 Find a n 2 n n 1 s n 4 n 6 7 n 2 5 5n2 2 The series n 1 an 10 Let be a series whose nth partial sum is sn a None of these 12 b converges to7 c converges to 2 5 d diverges 7 e converges to 5 11 Which sequence is both bounded and increasing a an sin 2n 2 b an 1 n c an ln n d an e n e None of these 1 1 x2 dx 12 Compute a 4 b None of these c 3 d 4 e 2 13 The sequence an a Converges to 3 b Converges to 0 c None of these d Diverges e Converges to 7 n 2 n 5 n2 n2 1 7 n 1 n 1 4 5n 14 Compute the sum of the series 16 a 9 b 20 9 c None of these d 16 9 e This series diverges 15 Which of the following statements is true regarding the improper integral 1 1 a The integral converges ex and because 1 1 ex dx and ex b The integral diverges because 1 1 c The integral converges because 1 ex dx and 1 ex 1 1 d The integral diverges because ex and e The integral converges to 0 16 Which of the following series diverges by the Test for Divergence n cos 2n 1 I a III only II 4 4 8 dx x x e 3n dx dx dx dx dx n 1 n 1 x x x x 1 1 1 1 1 1 1 ex x dx 1 1 x 1 dx converges 1 ex dx diverges 1 1 ex dx converges 1 dx diverges 1 x 1 1 arctan n III n 1 b II and III only c I and II only d II only e I II and III 9 x2 e 1 x ln x x2 4x 13 dx 17 Which of these substitutions would be used to evaluate a x 2 3 sec b x2 4x 13 tan c x 4 13 sec d none of these e x 2 3 tan 18 The improper integral 1 a converges to e 1 b diverges to c converges to 1 d converges to 1 e diverges to 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 19 6 points Find a general formula an for the sequence Assume the pattern continues and begins with n 1 216 125 64 27 8 17 13 9 5 21 PART II WORK OUT dx 1 10 20 5 points Determine whether the series converges or diverges Fully support your conclusion 32n5n n 1 21 6 points Determine whether the series converges or diverges Fully support your conclusion 2 1 ne n n 11 22 10 points Compute algebraically must be 1 x2 9 x4 dx In your final answer any trig or inverse trig expressions that can be rewritten 12 23 10 points Compute x2 7x 9 x 2 x 1 2 dx DO NOT WRITE IN THIS TABLE Question Points Awarded 1 18 19 20 21 22 23 …
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