True or false:

Question

a) if f(x) is continuous at a, then the limit of f(x) as x approaches a exists

b) if the limit of f(x) as x approaches a exists, then f(x) is continuous at a

My answer:
a) false
b) true

Answer 1

both wrong. Better review the definition of continuous.

sin(x)/x -> 1 as a limit as x->0, but 0/0 is not defined, so it is not continuous there.