# Question #f3eb0

##### 1 Answer

#### Explanation:

For

#lim_(x->2)f(x)# exists.#f(2)# exists (this is not a problem here since#f(x)# is clearly defined at#x = 2#

Let's investigate the first postulate. We know that for a limit to exist, **the left hand and right hand limits must be equal**. Mathematically:

This also shows why we're only interested in

We'll be attempting to find values of 'c' for which these limits are equal.

Going back to the piecewise function, we see that to the left of

So:

Evaluating the limits:

From here, it's just a matter of solving for

What have we found? Well, we've figured out a value for

To get a visual idea of how this works, check out this interactive graph I made. Pick different values of

Hope that helped :)