Question

Solve for L:
$L=\underset{x\to \pi /4}{lim}\frac{1-\tan x}{\pi -4x}$

• A. $\frac{3}{8}$
• B. $\frac{7}{8}$
• C. $\frac{5}{8}$
• D. $\frac{1}{8}$

Answer 1

Answer: (D)

$\frac{1}{8}$

We have,

$L={lim}_{x\to \frac{\pi }{4}}\left(\frac{1-\tan x}{\pi -4x}\right)$

Apply L-Hospital rule,

$L={lim}_{x\to \frac{\pi }{4}}\left(\frac{0-{\sec }^{2}x}{0-4}\right)$

$L={lim}_{x\to \frac{\pi }{4}}\left(\frac{{\sec }^{2}x}{4}\right)$

$L=\left(\frac{{\sec }^2\frac{\pi }{4}}{4}\right)$

$L=\left(\frac{\frac{1}{2}}{4}\right)$

$L=\frac{1}{8}$

Hence, this is the answer.