Problem 1: some limits.

1 . Parts a) and b) use l'H™pital's rule:

> limit( ln(x^3)/x^2, x=infinity);

> limit( arctan(2*x)/sin(x), x=0);

Part c can be converted with some algebra into one of the top-10 Taylor series, with x=2: Divide by 2 and add 1, and you get the series for exp(2):

> sum(2^(n+1) /n!, n=1..infinity);

This is the same as 2 exp(2) - 2 .