Question

Determine if f defined by
(? sin
if x0
f(x)=
X
0.
if x=0
is a continuous function?​

Answer 1

Answer:

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.