Question $3$

$3\mathrm{.}1$ Evaluate the $limit,\underset{x-}{lim}\frac{2x+1}{\sqrt[\phantom{2}]{x^2+3}}.$ Show all your calculations

$3\mathrm{.}2$ Draw the graph $of$ the function, that satisfies each $of$ the following conditions

$i.\underset{x2}{lim}f(x)=-1$

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

iii. $,\underset{x{0}^{-}}{lim}f(x)=$

$iv.f(2)=4$

$v.f(-1)=f(3)=0$

$vi.,f$ increases $on$ its entire domain

$b.$ Describe the continuity $of$ the function, $f(x).$

$3\mathrm{.}3$ Given the piecewise function,

$q(x)=\{\begin{array}{cc}-|x-2|+c,& x4\\ -x^2+11x-23,& x>4\end{array}$

$a.$ Calculate the value $cof$ that makes $q$ continuous.