Question

Evaluate $\underset{x\to 0}{lim}\frac{\sin x}{x}$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin x}{x}$
$=\underset{x\to 0}{lim}\frac{x-\frac{x^3}{3!}+\frac{x^5}{5!}-...........}{x}=\underset{x\to 0}{lim}(1-\frac{x^2}{3!}+\frac{x^4}{5!}-..........)=1$