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 write and apply L’Hopital’s rule to solve Related
![\[ \lim_{x \to \frac{\pi}{2}} \frac{\tan (3x)}{\tan x}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-c9c88f9182d013b4cc3d55ef1cc3a968_l3.png "Rendered by QuickLaTeX.com")
and apply L’Hopital’s rule to solve![\begin{align*} \lim_{x \to \frac{\pi}{2}} \frac{\tan (3x)}{\tan x} &= \lim_{x \to \frac{\pi}{2}} \left( \frac{\sin (3x)}{\cos (3x)} \cdot \frac{\cos x}{\sin x} \right) \\[9pt] &= \lim_{x \to \frac{\pi}{2}} \frac{ 3 \cos x \cos (3x) - \sin x \sin (3x)}{\cos x \cos(3x) - 3 \sin x \sin (3x)} \\[9pt] &= \frac{1}{3}. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-2094c547a5476bcf0773a5fe4d16e4f0_l3.png "Rendered by QuickLaTeX.com")
and apply L’Hopital’s rule to solve