Question

Evaluate $\underset{x\to \frac{3\pi }{4}}{lim}\frac{1+\sqrt[3]{3\tan x}}{1-2{\cos }^{2}x}$

• A. $-\frac{1}{3}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

Answer: (A)

$-\frac{1}{3}$

(Using L' Hospital's rule)
$\underset{x\to \frac{3\pi }{4}}{lim}\frac{1+(\tan x{)}^{1/3}}{1-2{\cos }^{2}x}=\underset{x\to \frac{3\pi }{4}}{lim}\frac{\frac{1}{3}\tan x^{\frac{-2}{3}}{\sec }^{2}x}{4\cos x\sin x}=-\frac{1}{3}$