Evaluating limits

Question

Evaluate the limit: lim theta approaches 0 tan(5theta)/ln(theta+1)

Answer 1

L'Hopital's rule

since the limit as-is approaches 0/0, you can take the derivative of top and bottom and try again

lim θ->0 of 5/(1/(θ+1)) = (5θ+5)/1

Now when you plug in 0, you don't get 0/0, you get 5/1 = 5