Show that the function $f(x) = \begin{cases} \frac{\cos x}{\frac{\pi}{2} - x}, & x \neq \frac{\pi}{2} \\ 1, & x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$.
Show Hint
This limit can also be solved using L'Hôpital's Rule because substituting $x = \frac{\pi}{2}$ yields a $\frac{0}{0}$ indeterminate form. Differentiating the numerator gives $-\sin x$ and the denominator gives $-1$. Evaluating $\frac{-\sin(\pi/2)}{-1} = 1$ confirms the answer instantly!