This is a question from a calculus sample test, and I can't figure out how to prove it. Can I get some help from you guys?
Definition of continuity that we've learned is $\lim_{x\to a} f(x) = f(a).$ If that holds, then $f$ is continuous at $a$.
The definition that we learned of a limit is:
For every $\epsilon > 0$, there exists $\delta > 0$ such that $|x - a| < \delta$ implies $|f(x) - L| < \epsilon$.
$\epsilon$ and $\delta$, as far as I can tell, are just variables, $a$ is what $x$ is approaching, and $L$ is the limit.