# Finding the limit of a function as x approaches a.

1. Apr 29, 2010

### S-z

For the function, f(x)=x^2 I need to find the limit as x approaches a. I am sure the limit is a^2, but how can I prove this, should I use the epsilon delta method? if so, am I to set delta to $$\sqrt{}epsilon$$?
thanks

2. Apr 29, 2010

### CompuChip

Why don't you try it.

Let $\epsilon > 0$ and set $\delta = \sqrt{\epsilon}$.
If $|x - a| < \delta$ then
$$|f(x) - a^2| = |x^2 - a^2| = \cdots \le \cdots \stackrel{?}{\le} \epsilon$$