Question

If \(f(x)\) is defined by \[ f(x)= \begin{cases} \dfrac{1-\tan x}{4x-\pi}, & x\ne \dfrac{\pi}{4},\; x\in\left[0,\dfrac{\pi}{2}\right] \\[6pt] k, & x=\dfrac{\pi}{4} \end{cases} \] and \(f(x)\) is continuous in \[ \left[0,\frac{\pi}{2}\right], \] then \(k=\)

• A. \(-1\)
• B. \(-\dfrac{1}{2}\)
• C. \(\dfrac{1}{2}\)
• D. \(1\)

Hint:

For piecewise functions, continuity at the joining point requires that the function value equals the limit. When the limit gives the indeterminate form \(\frac{0}{0}\), L'Hospital's Rule is often the quickest method.

Answer 1

The Correct Option is B