009A Sample Midterm 1, Problem 3

Consider the following function  $f:$

$f(x)=\left\{{\begin{array}{lr}x^{2}&{\text{if }}x<1\\{\sqrt {x}}&{\text{if }}x\geq 1\end{array}}\right.$

(a) Find  $\lim _{x\rightarrow 1^{-}}f(x).$

(b) Find  $\lim _{x\rightarrow 1^{+}}f(x).$

(c) Find  $\lim _{x\rightarrow 1}f(x).$

(d) Is  $f$  continuous at  $x=1?$  Briefly explain.

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