Plugin-e1_prac_S2010 - k is(A 16 15(B 13 16(C 12 15(D 17 16(E divergent 9 lim x → 3 x sin x =(A 3 e(B 3(C 6 e(D 6(E 3 e 10 A sequence is deFned

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M408D Practice problems for Exam #1 Directions . Indicate the correct answer for each problem by Flling in the appropriate space, as in (A) ( ) (C) (D) (E). 1) If lim x c f ( x ) = 1 and lim x c g ( x ) = 0, then which of the following limits is indeterminate? (A) lim x c f ( x ) g ( x ) . (B) lim x c sin( g ( x )) f ( x ) . (C) lim x c 1 - f ( x ) g ( x ) . (D) lim x c g ( x ) f ( x ) . (E) lim x c f ( x ) g 2 ( x ) . 2) i 2 -∞ xe x/ 4 dx = (A) e 16 . (B) 4 e . (C) - 8 e . (D) - 2 e 2 . (E) - 4 e 2 . 3) Which of the following statements about the sequence a n = n + 1 n , n 1, is true ? (A) it is increasing and bounded. (B) it is increasing but not bounded. (C) it is decreasing and bounded. (D) it is bounded but not monotonic. (E) it is not bounded and not monotonic. 4) lim n →∞ n ln p 1 + 3 n P = (A) 0. (B) 1 3 . (C) - 3 2 . (D) 3. (E) . 5) lim x →∞ xe 6 /x - x = (A) 3. (B) 6. (C) - 1 6 . (D) - 1 3 . (E) . 6) What are all values of r for which the sequence a n = ln( n ) n r , n 1, is convergent? (A) r > 0. (B) - 1 < r 1. (C) 0 r 2. (D) 0 < r < 1. (E) r < 0.
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7) i e 1 x ln x dx = (A) 1. (B) -∞ . (C) 1 2 . (D) - 3. (E) . 8) The sum of the series s k =0 p 1 4 P 2
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Unformatted text preview: k is: (A) 16 15 . (B) 13 16 . (C) 12 15 . (D) 17 16 . (E) divergent. 9) lim x → + 3 x sin( x ) = (A) 3 e . (B) 3. (C) 6 e . (D) 6. (E) 3 e . 10) A sequence is deFned by a n +1 = 1 / (1 + a n ), a 1 = 1, n ≥ 1. Assuming this sequence is convergent, its limit is: (A) √ 3-1 2 . (B)-√ 5-1 2 . (C) 1. (D) 1 2 . (E) √ 5-1 2 . 11) A sequence a k ( k ≥ 1) with partial sums s n ( n ≥ 1) satisFes a k > 0 and s n ≤ 5 for all k and n . Which of the following statements may be false ? (A) s n is increasing. (B) s n is bounded above. (C) a k is monotonic. (D) ∞ s k =1 a k converges. (E) s n is bounded below. 12) If ∞ s k =2 Q p 1 5 P k = 1 12 , then the value of the constant Q must be: (A) 5 3 . (B) 3 2 . (C) 4 9 . (D) 1 6 . (E) 2 5 ....
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This note was uploaded on 01/27/2011 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas at Austin.

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Plugin-e1_prac_S2010 - k is(A 16 15(B 13 16(C 12 15(D 17 16(E divergent 9 lim x → 3 x sin x =(A 3 e(B 3(C 6 e(D 6(E 3 e 10 A sequence is deFned

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