Question

If lim x->6 f(x)g(x) exists, then the limit must be f(6)g(6). True or false?

Explain why it's true or false.

Help!

Answer 1

It is possible that the lim x→q f(x) exists, but f(q) does not.

An example is
f(x)=sin(x)/x where
lim x→0 f(x)=1, but
f(0) does not exist.

I leave it up to you to decide on whether the answer should be true or false.