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# 2JSF2 - SECOND SAMPLE FINAL FOR MATH 2J This sample 2J...

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SECOND SAMPLE FINAL FOR MATH 2J This sample 2J final exam is meant for practice only. Length and content of the actual final may vary, at the discretion of the instructor. Try to complete the test in 1 hour and 50 minutes, without consulting any book or notes, and without using a calculator. 1

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2 PROBLEM 1 ( True/False Questions ) If 0 a n b n and n =1 b n converges, then n =1 a n converges. true false If 0 a n b n and n =1 b n diverges, then n =1 a n diverges. true false n =0 2 n n ! = e 2 . true false 1 x + 2 x + 3 x + . . . is a power series. true false If P 3 ( x ) = 4 + 2 x - x 2 is the 2 nd -degree Taylor polynomial of a function f at a = 0, then f 0 (0) = 2 . true false If { a n } is decreasing and a n > 4 for all n , then { a n } is convergent. true false If a n > 0 and n =1 a n converges, then n =0 ( - 1) n a n converges absolutely. true false If 0 < α < 1, then lim n →∞ α n = 0 . true false
3 PROBLEM 2 Determine whether the sequence is convergent or divergent .

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