(tanx+sqrt(3))/(x-2pi/3)

Question

What is the limit as x approaches 2pi/3.

Answer 1

This sounds like a straight up homework question, and I'm pretty sure I'm not supposed to just give a straight up answer. So I'll say if you evaluate at x=2pi/3 you get 0/0 so once you see that you know to use l'Hopitals rule. Take the derivative of the top and bottom separately and then evaluate the ratio of THOSE at 2pi/3.