Question

Function $\left\{ \begin{matrix} 2x\tan x–\frac{\pi}{\cos x}; & x \neq \frac{\pi}{2} \\ k & þ \end{matrix} = \frac{\pi}{2} \right.\$ is continuous at x = $\frac{\pi}{2}$if k =

• A. – 2
• B. 2
• C. $\frac{1}{2}$
• D. No such values of k exists

Answer 1

Answer: (A)

– 2

Answer 2

$\underset{x \rightarrow \pi/2}{Lt}\left( 2x\tan x–\frac{\pi}{\cos x} \right)$=$\underset{x \rightarrow \pi/2}{Lt}\frac{2x\sin x–\pi}{\cos x}$

= –2 (using L’Hospital rule)