WUSTL MATH 132 - math132-fall2016-Exam3 (11 pages)

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math132-fall2016-Exam3

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Pages:
11
School:
Washington University in St. Louis
Course:
Math 132 - Calculus II
Calculus II Documents

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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



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