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  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\rightarrow 1} f(x).}

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

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