Sorry for posting so many of these! I'm finding them a little tricky and keep running into problems

I've done two proofs for this, one uses

and

, the other uses sequences.

The epsilon-delta version:

I need to find

when

.

Since i'm trying to find continuity at 0, let

.

Therefore I need to find

when

.

For

,

. Hence pick

.

For

,

. Hence pick

Therefore choose

That was preliminary work so I have to write out the proper proof:

Let

and define

. When

:

for

.

for

.

Hence f is continuous

.

Thanks in advance to anyone who posts!