Question

$\underset{x\to 0}{\lim }\left(\frac{\tan x}{\sqrt{2x+4}-2}\right)$ is equal to

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

Answer: (A)

$\underset{x\to 0}{\lim }\left(\frac{\tan x}{\sqrt{2x+4}-2}\right)\left[\frac{0}{0}\right]$ form
Applying L' Hopitals' rule, we get
$\underset{x\to 0}{\lim }\left(\frac{{\sec }^{2}x}{\frac{2}{2x\sqrt{2x+4}}-0}\right)$
$=\underset{x\to 0}{\lim }\left((\sqrt{2x+4}){\sec }^{2}x\right)$
$=\sqrt{2\times 0+4}\times 1=2$