Question

$\underset{x\to 0}{lim}\frac{\sin 4x}{1-\sqrt{1-x}}$ is

• A. $4$
• B. $8$
• C. $10$
• D. $2$

Answer 1

The correct option is B $8$

Substituting gives us indeterminate form.
So, applying L'Hospital's Rule,
${lim}_{x\to 0}\frac{4\cos 4x}{\frac{1}{2\sqrt{(1-x)}}}$
$=\frac{4\times 1}{\frac{1}{2}}$
$=8$
Hence, option 'B' is correct.