plugin-e1_prac_S2010 - k is(A 16 15(B 13 16(C 12 15(D 17...

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M408D Practice problems for Exam #1 Directions . Indicate the correct answer for each problem by filling 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) integraldisplay 2 -∞ xe x/ 4 dx = 3) Which of the following statements about the sequence a n = n + 1 n , n 1, is true ? 4) lim n →∞ n ln parenleftBig 1 + 3 n parenrightBig = 5) lim x →∞ xe 6 /x - x = 6) What are all values of r for which the sequence a n = ln( n ) n r , n 1, is convergent?
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7) integraldisplay e 1 x ln x dx = 8) The sum of the series summationdisplay k =0 parenleftbigg
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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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