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JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Mathematics
Chapter
Limits

JEE Main 2004 · Mathematics · Limits

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

Let f(x)=1−tan⁡x4x−π,x≠π4,x∈[0,π2]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)f(x) is continuous in \left[0, \frac{\pi}{2}\right],then, thenf\left(\frac{\pi}{4}\right)$ is

Options

  1. A1
  2. B12\frac{1}{2}
  3. C−12-\frac{1}{2}
  4. D−1-1

Correct answer

C. −12-\frac{1}{2}

Step-by-step solution

f(x)=1−tan⁡x4x−π⇒lim⁡x→π41−tan⁡x4x−π=−12f(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}
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