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Quiz!!!

Quiz!!!. Which sequence converges? an = n+3/n an = -1+(-1)^n/n an = n/lnn an = n!/3^n Answer: B. 2. Which of the following sequences diverges? A. an = 1/n B. an = 2^n/e^n C. an = n^2/e^n D. an = n/lnn Answer: D. 3. The sequence {r^n} converges if and only if IrI<1 IrI<=1 -1<r<=1

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Quiz!!!

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  1. Quiz!!!

  2. Which sequence converges? • an = n+3/n • an = -1+(-1)^n/n • an = n/lnn • an = n!/3^n Answer: B

  3. 2. Which of the following sequences diverges? A. an = 1/n B. an = 2^n/e^n C. an = n^2/e^n D. an = n/lnn Answer: D

  4. 3. The sequence {r^n} converges if and only if • IrI<1 • IrI<=1 • -1<r<=1 • 0<r<1 Answer: C

  5. 4. If the series tan^(-1)=1-1/3+1/5-1/7+… is used to approximate Π/4 with error less than 0.001, then the smallest number of terms needed is • 100 • 200 • 400 • 500 Answer: D

  6. 5. The coefficient of (x-Π/4)^3 in Taylor series about Π/4 of f(x)=cosx is A.(√3)/12 B. -1/12 C. 1/12 D. 1/ (6√2) Answer: D

  7. 6. Which of the following series can be used to compute ln0.8? • ln(x-1) expanded around x=0 • lnx about x=0 • lnx expanded about x=1 • none of these Answer: C

  8. 7. The sum of the series ∞ ∑(Π^3/3^Π)^n is equal to n=1 • 0 B. 1 C. Π^3/(3^Π-Π^3) D. none of these Answer: C

  9. 8. The set of all values of x for which ∞ ∑n*2^n/x^n converges is n=1 • only x=0 B. IxI=2 C. IxI>2 D. none of these Answer: C.

  10. 9. The coefficient of (x-1)^5 in the Taylor series for xlnx about x=1 is • -1/20 • 1/5! • -1/5! • 1/4! Answer: A.

  11. 10. The coefficient of x^2 in the Maclaurin series or e^(sinx) is • 0 • 1 • 1/2! • -1 Answer: C

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