Question $3$

$15$ Marks

$3\mathrm{.}1$ Evaluate the limit$,\underset{x-}{lim}\frac{2x1}{\sqrt[\phantom{2}]{x^{2}3}}.$ Show all your calculations

$(5$ Marks$)$

$2\mathrm{.}1$ Draw the graph of the function, that satisfies each of the following conditions

$(4$ Marks$)$

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, $f(x).$

$(1$ Mark$)$

$2\mathrm{.}1$ Given the piecewise function,

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

a$.$ Calculate the value $c$ of that makes $q$ continuous.

$(5$ Marks$)$

End of Question $3$