Math 132 Exam 3 Fall 2016 15 multiple choice questions worth 5 points each 2 hand graded questions worth 12 and 13 points each Exam covers sections 11 1 11 6 Sequences Series Integral Comparison Alternating Absolute not Root or Ratio No calculators For the multiple choice questions mark your answer on the answer card Show all your work for the written problems Your ability to make your solution clear will be part of the grade Useful Formulas Pn i 1 Pn i 1 i3 Pn n n 1 2 i n n 1 2 i 1 2 i2 n n 1 2n 1 6 sin2 cos2 1 1 tan2 sec2 1 cot2 csc2 sin A B sin A cos B sin B cos A cos A B cos A cos B sin A sin B tan A B cos A cos B R 1 2 tan A tan B 1 tan A tan B cos A B cos A B sin A sin B 1 2 cos A B cos A B sin A cos B 1 2 sin A B cos A B sin2 x 12 1 cos 2x cos2 x 21 1 cos 2x sin 2 2 sin cos cos 2 cos2 sin2 csc x dx ln csc x cot x C R sec x dx ln sec x tan x C Math 132 Exam 3 Page 2 of 11 1 Determine whether the sequence defined by an ln 2n3 2 ln 5n3 2n2 4 converges or diverges If it converges find the limit A 0 B ln 2 5 C ln D 2 5 2 5 E 2 F 5 G Diverges 2 Find ALL possible values of x for which the series X 9 xn n 0 5n converges A It is not possible to find such x because the series diverges B x 0 C x 1 D 3 x 3 E 3 x 5 F 5 x 5 G x Math 132 Exam 3 Page 3 of 11 3 Determine whether the sequence defined by 2 2 an n cos n2 2 converges or diverges If it converges find the limit A 2 B 1 C 0 D 1 E 2 F G Diverges 4 Which of the following sequences converge an 2n 1 n 4 bn A dn only B an bn only C cn dn only D an dn only E an bn dn only F an cn dn only G All of them n n100 cn ln n10 n dn n4 n 1 Math 132 Exam 3 5 Assume the terms of a sequence an are given by the following formula an 1 22 32 n2 3n3 3n3 3n3 3n3 Find the limit of the sequence or conclude that it diverges A 0 B 1 C D E F 1 2 2 3 1 6 1 9 G Diverges 6 Determine the value of the series X n 2 6 n n 3 or conclude that it diverges A 0 B C D E F 13 2 5 3 13 6 13 3 10 2 G Diverges Page 4 of 11 Math 132 Exam 3 Page 5 of 11 7 Determine the value of the series X 2n 2 3n 1 4n n 0 or conclude that it diverges A 4 B C D E F 9 2 13 2 37 4 25 2 97 8 G Diverges 8 Assume X an is an infinite series with partial sums given by SN 4 n 1 A B C D E F G H 22 5 2 5 1 10 3 10 92 52 1 10 3 10 2 N What is a5 Math 132 Exam 3 Page 6 of 11 9 Which of the following series converge I X 1 n n 1 1 1 n II X n 2 1 ln n4 III X n 1 A None of them B I only C II only D III only E I and II F I and III G II and III H All of them 4 X X 4 2 1 Find the value of the series 10 The series 4 n 90 n n 2 n 1 A B C D E F G 8 4 45 8 4 1 45 4 16 1 90 2 8 4 90 8 4 16 90 Diverges n n2 1 Math 132 Exam 3 Page 7 of 11 11 Which of the following series converge I X 2n n4 n 1 4n n2 II X n 1 4n 5n n III X n 3n n 1 A None of them B I only C II only D III only E I and II F I and III G II and III H All of them 12 Which of the following series converge I X ln n n e 2 n 1 A None of them B I only C II only D III only E I and II F I and III G II and III H All of them II X sin2 n n n3 2 n 2 III X 1 n n 1 n2 3 Math 132 Exam 3 Page 8 of 11 13 Which of the following alternating series converge conditionally but not absolutely I X 1 n n ln n n 2 II X 1 n n ln n 2 n 2 III A None of them B I only C II only D III only E I and II F I and III G II and III H All of them 14 For which values of p does the series X n 1 A All values of p B 1 p 1 C p 1 D p 1 E p F p 1 2 1 2 G No values of p en converge 2 e2n p X cos n n 1 2n 3 Math 132 15 Let Exam 3 X an be a series with partial sums SN Which of the following statements are n 1 always true I If lim an 0 then n II If X X X an converges n 1 an L then lim an L n n 1 III If Page 9 of 11 an converges then lim an 0 n n 1 IV If lim SN L then N A None of them B I and II C I and III D II and III E III and IV F I II IV G II III IV H All of them X n 1 an L Math 132 Exam 3 Page 10 of 11 Name ID Discussion Section Letter You can find your discussion section on the front of your exam book Written Problem You will be graded on the readability of your work Use the back of this sheet if necessary 16 Determine whether the following series converge or diverge State any tests used and show that all conditions of the test are satisfied a X ln n n 3 b X n 1 n2 3n 5n n3 Math 132 Exam 3 Page 11 of 11 Name ID Discussion Section Letter You can find your discussion section on the front of your exam book Written Problem You will be …
View Full Document
Unlocking...