Lim sin(60-x)/2cosx-1 x approaches 60

Answer 1

Use L'Hopitals rule

Lim sin(60°-x)/(2cosx - 1)
= lim sin(π/3-x)/(2cosx - 1) , as x --> π/3
= lim cos(π/3 - x)/(-2sinx) as x---> π/3
= cos 0/(-2sin(π/3
= 1/(-2(√3/2)
= -√3 or appr -.5773

http://www.wolframalpha.com/input/?i=y+%3D+sin%28%CF%80%2F3-x%29%2F%282cosx-1%29+

notice the vertical asymptote at appr -.5

Answer 2

I WAS STRUGGLING WITH THIS PROBLEM SO BUT FROM NOW ONWARD I WILL BEAR THIS AT THE BACK OF MY MIND