Unformatted text preview: QUESTION 3. (6 + 6 = 12 pts) (i) Determine whether the improper integral Z ∞ e2 x dx converges. Evaluate the integral if it is convergent. (ii) Giving reasons for your answer discuss the convergence of the improper integral Z ∞ 1 sin 2 x x 2 + 1 dx QUESTION 4. (2 + 4 + 4 + 4 = 14 pts) (i) Deﬁne what it means for the number L to be a limit of the sequence { a n } ∞ n =1 . (ii) Prove the following limit using the formal deﬁnition. lim n →∞ 1 4 n + 3 = 0 . (iii) Determine whether the sequence a n = n sin(1 /n ) converges. If it converges, ﬁnd the limit. (iv) Determine whether the sequence a n = ( n +1) ( n +3) is increasing, decreasing or not monotonic. Is the sequence bounded? 1...
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This note was uploaded on 06/04/2011 for the course MAC 3473 taught by Professor Block during the Fall '08 term at University of Florida.
 Fall '08
 BLOCK
 Calculus, Integrals

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