- #1

Frillth

- 80

- 0

1. Prove whether:

sum from x=1 to infinity of x!*10^x/x^x

converges or diverges

2. Prove whether:

sum from x=3 to infinity of sqrt(m+4)/(m^2-2m)

converges or diverges

3. Calculate the Maclaurin series of f(x)=3x^2*cos(x^3) Hint: Explicity use the Maclaurin series for cosine.

4. Using the series from 3, verify that the integral of 3x^2*cos(x^3)dx = sin(x^3) + C

For 1 and 2, I believe we're supposed to use the integral test, comparison test, root test, or ratio test. For 3 and 4, I'm not quite sure even how to start. We had about 15 problems of homework, but these are the only ones that are giving me trouble. Can anybody help me out?