MATH 141E Fall 2005 Midterm 2

# MATH 141E Fall 2005 Midterm 2 - MATH 141 1. Find lim ex - 1...

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MATH 141 EXAMINATION II, FORM A NOVEMBER 8, 2005 1. Find lim x 0 e x - 1 - x 5 x 2 . a) 5 b) c) 0 d) -∞ e) 1 10 2. Find lim x →-∞ x 9 e x . a) 0 b) 9 c) d) 1 9 e) -∞ 3. Evaluate the integral I = Z 0 e - 2 x dx . a) I = 2 b) I = 1 2 c) I = - 1 2 d) The integral is divergent. e) I = - 2 4. Which of the following integrals is convergent? a) Z 7 0 4 dx x b) Z 0 - 7 2 dx x 2 c) Z 7 0 5 6 dx x x d) Z 7 0 7 x dx e) All of these integrals are divergent. 5. Determine whether the sequence 5 n 6 n +1 f converges or diverges. If it converges, ±nd the limit. a) converges; limit = 1 b) converges; limit = 5 36 c) converges; limit = 0 d) converges; limit = 5 6 e) diverges 6. Determine whether the series X n =1 9 - n 10 n +1 is convergent or diver- gent. If it is convergent, ±nd its sum. a) 76 b) 106 c) 60 d) 90 e) divergent 7. Find the values of p for which the series X m =5 1 m ln m [ln(ln m )] p is convergent. a)

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## This note was uploaded on 04/12/2008 for the course MATH 141E taught by Professor Spaeth during the Spring '08 term at Pennsylvania State University, University Park.

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MATH 141E Fall 2005 Midterm 2 - MATH 141 1. Find lim ex - 1...

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