Question

Solve $\underset{x\to 0}{lim}\frac{x}{4x-\tan 5x}$

Answer 1

The given limit can be simplified as

$\underset{x\to 0}{lim}\frac{x}{4x-\tan 5x}$

$=\frac{0}{0}$

This is the indeterminate form, therefore, apply L’Hospitals rule.

$\underset{x\to 0}{lim}\frac{1}{4-5{\sec }^{2}5x}$

$=\frac{1}{4-5\left(1\right)}$

$=-1$