Let f(x)=(1-tan x)/(4 x-π), x ≠ (π)/4, x ∈ [0, (π)/2 ] . If f(x) is continuous in [0, (π)/2 ] , then f ((π)/4 ) is

Correct answer: (C) -1/2. f(x)=(1-tan x)/(4 x-π) ⇒ lim _x arrow (π)/4 (1-tan x)/(4 x-π)=-1/2

Q104 / 225 · JEE Main 2004 · Mathematics

Let $f(x)=\frac{1-\tan x}{4 x-\pi}, x \neq \frac{\pi}{4}, x \in\left[0, \frac{\pi}{2}\right]$. If $f(x)$ is continuous in $\left[0, \frac{\pi}{2}\right]$, then $f\left(\frac{\pi}{4}\right)$ is

$f(x)=\frac{1-\tan x}{4 x-\pi} \Rightarrow \lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{4 x-\pi}=-\frac{1}{2}$

Hence, the correct answer is option: 'C'.