Question

Discuss the continuity of the function f (x)=sin2x-1 at the point x=0 and x=pie

Answer 1

At x=0 it has a very pointy change! But it is still defined at x=0, because f(0)=0 (so no "hole"), And the limit as you approach x=0 (from either side) is also 0 (so no "jump"), So it is in fact continuous.