$1-.$ Given

$f(x)=\{\begin{array}{ccc}{x}^2+1& if& x<mn>0</mn>\\ 0& if& x=0\\ 1-x& if& x>0\end{array}$

Find $\underset{x0}{lim}f(x).$ Show your work. $[4]$

$2-.$ Let

$f(x)=\{\begin{array}{ccc}1-x^2& if& x0\\ 2x-1& if& x<mn>0</mn>\end{array}$

a$)$ Find the following limits$,$ if they exist. $[6]$

i$)\underset{x{0}^{+}}{lim}f(x)$

ii$)\underset{x{0}^{-}}{lim}f(x)$

iii$)$

b$)$ Sketch the graph of $f(x).$ Label properly. $[4]$

$3.$ Determine the following limits$.[16]$

a$)\underset{x3}{lim}[2x^3+5x-\sqrt[\phantom{2}]{-x^2-2x+24}]$

b$)\underset{x16}{lim}\frac{4\sqrt[\phantom{2}]{x}-x}{x-16}$

c$)\underset{x0\mathrm{.}5}{lim}\frac{8x^3-1}{10x^3-5x^2-6x+3}$

d$)\underset{x{3}^{-}}{lim}\frac{|x-3|}{x^2-9}$