Question

$\underset{x\to 0}{lim}\frac{\sin 4x}{1-\sqrt{(1-x)}}$ equals

• A. $4$
• B. $8$
• C. $10$
• D. None of the above

Answer 1

Answer: (B)

$8$

$\underset{x\to 0}{lim}\frac{sin4x}{1-\sqrt{(1-x)}}$
$=\underset{x\to 0}{lim}\frac{sin4x}{1-\sqrt{(1-x)}}.\frac{1+\sqrt{(1-x)}}{1+\sqrt{(1-x)}}$
$=\underset{x\to 0}{lim}\frac{sin4x}{1-(1-x)}.(1+\sqrt{(1-x)})$
$=\underset{x\to 0}{lim}4\frac{sin4x}{4x}.(1+\sqrt{(1-x)})=4\times 2=8$