Home » Blog » Compute the limit of the given function Compute the limit of the given function by RoRi December 25, 2015 Evaluate the limit. We use the definitions of and to write Related
![\[ \lim_{x \to \frac{\pi}{2}} \frac{\tan x - 5}{\sec x + 4}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-038025f489388e2f15fd4b56562816bf_l3.png "Rendered by QuickLaTeX.com")
and 
to write![\begin{align*} \lim_{x \to \frac{\pi}{2}} \frac{ \tan x - 5}{\sec x - 4} &= \lim_{x \to \frac{\pi}{2}} \frac{ \frac{\sin x}{\cos x} - 5}{\frac{1}{\cos x} - 4} \\[9pt] &= \lim_{x \to \frac{\pi}{2}} \frac{\sin x - 5 \cos x}{1 - 4 \cos x} \\[9pt] &= 1. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-1274ce964449d825956f748687a2fd2f_l3.png "Rendered by QuickLaTeX.com")
and to write