Originally Posted by

**chukie** $\displaystyle k(x)$ is a piecewise function

$\displaystyle k(x) =

\left\{\begin{array}{rl}

\frac{x^2-2b+b^2}{x-b}, & \text{if }x\neq a\\

5, & \text{if }x=a

\end{array}\right.$

then which of the following is true about $\displaystyle k(x)$:

1) $\displaystyle \lim_{x\to a}k(x)\text{ exists}$

2) $\displaystyle k(x) \text{ is continuous at }x=a$

3) $\displaystyle k(a) \text{ exists}$

so far i think that $\displaystyle k(a)$ will exist because it will equal 5 right? realli not sure about the other two.