Let $f(x)=\frac{1- an x}{4 x-\pi}, x
eq \frac{\pi}{4}, x \in\left[0, \frac{\pi}{2} ight]$. $f(x)

Question

Let $f(x)=\frac{1-	an x}{4 x-\pi}, x 
eq \frac{\pi}{4}, x \in\left[0, \frac{\pi}{2}ight]$. $f(x)$ is continuous in $\left[0, \frac{\pi}{2}ight]$, then $f\left(\frac{\pi}{4}ight)$ is\

Professor PC Thomas Classes · Answer

(a) : $\lim _{x ightarrow \pi / 4} \frac{1-	an x}{4 x-\pi}$\ $	herefore \quad \lim _{x ightarrow \pi / 4} \frac{(1-	an x) 	imes(1+	an x)}{(1+	an x)\left[-4\left(\frac{\pi}{4}-xight)ight]}$\ $=\lim _{x ightarrow \pi / 4}-\frac{	an \left(\frac{\pi}{4}-xight) 	imes(1+	an x)}{4\left(\frac{\pi}{4}-xight)}=-\frac{1}{2}$\