QUESTION $1$

$1\mathrm{.}1$ Find only $y$ using Cramer's rule given the following simultaneous equations

$y+2x-z=-3$

$3y+x+z=4$

$y-x+2z=6$

$1\mathrm{.}2$ Use the binomial theorem to write down the first four terms in the expansion of

$(1+y{)}^{-\frac{1}{3}}$

$1\mathrm{.}3\mathrm{.}1$ Resolve $\frac{x^2+1}{x(x^2-1)}$ fully into partial fractions.

$1\mathrm{.}3\mathrm{.}2$ Now determine ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2+1}{x(x^2-1)}dx$

$[20]$

QUESTION $2$

$2\mathrm{.}1$ Find $Z=\frac{Z_1{Z}_2}{Z_1+Z_2}$ if $Z_1=3\mathrm{.}1618\mathrm{.}4$ and $Z_2=4\mathrm{.}4763\mathrm{.}4.$

$2\mathrm{.}2$ Convert $2e^{\frac{}{2}j}$ to rectangular form.

$2\mathrm{.}3$ Find the three distinct roots of the equation $Z^3+27=0.$

$2\mathrm{.}4$ Determine the equation of the circle with centre $(2,-3)$ and radius $\sqrt[\phantom{2}]{3}.$

$(6)$

$(3)$

$[17]$

QUESTION $3$

$3\mathrm{.}1$ Determine the following limit: $\underset{x3}{lim}\frac{x^2-9}{x-3}$

$3\mathrm{.}2$ Differentiate the following with regard to $x$ :

$3\mathrm{.}2\mathrm{.}1y=\sqrt[\phantom{2}]{1-3x^4}$

$3\mathrm{.}2\mathrm{.}2y=(e^{3x})(cos(x^2+1))$

$3\mathrm{.}2\mathrm{.}3y=\frac{2x}{1-x^2}$ Simplify your answer.

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