Quiz!!!

1. Which sequence converges?

A. an = n+3/n

B. an = -1+(-1)^n/n

C. an = n/lnn

D. 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

A. IrI<1B. IrI<=1C. -1<r<=1D. 0<r<1

Answer: C

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

A. 100

B. 200

C. 400

D. 500

Answer: D

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

6. Which of the following series can be used to compute ln0.8?

A. ln(x-1) expanded around x=0

B. lnx about x=0

C. lnx expanded about x=1

D. none of these

Answer: C

7. The sum of the series ∞∑(Π^3/3^Π)^n is equal ton=1

A. 0 B. 1C. Π^3/(3^Π-Π^3) D. none of these

Answer: C

8. The set of all values of x for which

∞

∑n*2^n/x^n converges is

n=1

A. only x=0 B. IxI=2

C. IxI>2 D. none of these

Answer: C.

9. The coefficient of (x-1)^5 in the Taylor series for xlnx about x=1 is

A. -1/20

B. 1/5!

C. -1/5!

D. 1/4!

Answer: A.

10. The coefficient of x^2 in the Maclaurin series or e^(sinx) is

A. 0

B. 1

C. 1/2!

D. -1

Answer: C