# How do you find lim cos(3theta)/(pi/2-theta) as theta->pi/2 using l'Hospital's Rule?

Oct 17, 2017

Look below

#### Explanation:

You need to see if the limit is in indeterminate form, so calculate the limit as $\theta \to \frac{\pi}{2}$

$\cos \frac{3 \left(\frac{\pi}{2}\right)}{\frac{\pi}{2} - \frac{\pi}{2}} = \frac{0}{0}$ which is indeterminate form

now do the derivative of the function

${\lim}_{\theta \to \frac{\pi}{2}} \frac{d}{\mathrm{dx}} \left[\cos \frac{3 \theta}{\frac{\pi}{2} - \theta}\right]$

$\frac{d}{\mathrm{dx}} \left[\cos \left(3 \theta\right)\right] = 0$

$\frac{d}{\mathrm{dx}} \left[\frac{\pi}{2} - \theta\right] = 0$

$\frac{0}{0}$ is indeterminate form

so the limit doesn't exist