Chapter 3.6, Problem 2ES

Evaluate the given limit without using L’Hopital’s rule, and then check that your answer is correct using L’Hopital’s rule.

(a) $\underset{x\to 0}{\lim }\frac{\sin x}{\tan x}$

(b) $\underset{x\to 1}{\lim }\frac{x^2-1}{x^3-1}$