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

1 Answer
Oct 17, 2017

Look below

Explanation:

You need to see if the limit is in indeterminate form, so calculate the limit as theta -> pi/2

cos(3(pi/2))/{pi/2-pi/2} = 0/0 which is indeterminate form

now do the derivative of the function

lim_{theta->pi/2} d/dx[cos(3theta)/{pi/2-theta}]

d/dx [cos(3theta)] = 0

d/dx [pi/2-theta] = 0

0/0 is indeterminate form

so the limit doesn't exist