Explanation

(c)
$\lim_{x \rightarrow \frac{\pi}{4}\ }\frac{\tan{x - 1}}{x - \frac{\pi}{4}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\lbrack \frac{0}{0}\ from \right\rbrack$
Applying L’Hospital’s rule,
$= \lim_{x \rightarrow \frac{\pi}{4}\ } = \frac{\sec^{2}x}{1} = 2$