Which of the following functions with domain R-{0} have a limit at 0 and what is it?

(1) f(x)=x

(2) f(x)=1/x

How would I prove these either using the definition of limit, the Sequential Criterion for limits, or the Squeeze thm for limits of functions?

For number (1), is this on the right track?

Let

>0 be given. Suppose that

=

. Then if |x|<

, |f(x)|=|x|<

is true.

Is that correct for number 1? and how would I go about proving #2? I know that it goes to 0 because of the squeeze theorem but how do I write a formal proof for that?

Thanks