Question

Evaluate limit as x approaches 0 sin^2x/(1-cosx).

Answer 1

`\lim_(x \to 0) (sin ^(2)x )/(1-cos x) = ( (0)/(0) )= \\ = \lim_(x \to 0) (1-cos ^(2)x )/(1-cosx)= \\ = \lim_(n \to 0) ((1+cosx)(1-cosx))/((1-cosx))= \\ = \lim_(x \to 0) (1+cos x) =`
= 1 + cos 0 = 1 + 1 = 2