Question

Evaluate $\underset{x\to 0}{lim}\frac{\sin 4x}{x}$

Answer 1

We have, $\underset{x\to 0}{lim}\frac{\sin 4x}{x}$

Multiplying the numerator and the denominator by $4$ produces

$=\underset{x\to 0}{lim}\frac{4\sin 4x}{4x}$

$=4\underset{x\to 0}{lim}\frac{\sin 4x}{4x}$

$=4$...........[ $\underset{x\to 0}{lim}\frac{\sin y}{y}=1$]