QUESTION $4$

$4\mathrm{.}1$ Expand $(x-2{)}^5$ to four terms.

$4\mathrm{.}2$ Determine $\underset{t2}{lim}(\frac{t^3-8}{t-2}).$

$4\mathrm{.}3$ Differentiate $y=\sqrt[\phantom{2}]{cosecx},$ using a function of a function $($chain rule$).$

$4\mathrm{.}4$ Differentiate $y=\frac{lntanx}{lnx}$ using a quotient rule.

$4\mathrm{.}5$ Differentiate with respect to $y$ :

$x=\frac{y^2}{2}-2lny+cosecy-\frac{1}{coty}+2k-\frac{1}{cosecy}+\frac{5^3}{2}-\frac{1}{4e^{91}}$

$[25]$