1Express $r(\cos\theta +i\sin \theta)$ in the exponential form
$re^{i\theta}$
2Express
$\cos\theta$
in the exponential form
$\frac{e^{i\theta}+e^{-i\theta}}{2}$
3Express
$i\sin\theta$
in the exponential form
$\frac{e^{i\theta}-e^{-i\theta}}{2}$
4State De Moivre's theorem
$z^n=r^n(\cos n\theta+i\sin n\theta)$
5What is the method for evaluating an indefinite integral?
For the value for which the integrand is undefined, substitute the value for a variable and consider the value of the integral as that variable tends to the original value
6What is the equation for determining the mean value of a function $f(x)$
$\mathcal{\overline{f(x)}=\frac{1}{b-a}\int_{a}^{b} f(x).dx}$
7Express $\mathcal{\frac{px^2+qx+r}{(x+a)(x^2+bx+c)}}$ in partial fractions
${\frac{A}{\mathcal{x-a}}+\frac{B\mathcal{x}+C}{\mathcal{x^2+bx+c}}}$
8What is the solution to
$\mathcal{\int{(ax+b)^n}.dx}$
$\mathcal{\frac{(ax+b)^{n+1}}{a(n+1)}+c}$
9What is the solution to
$\mathcal{\int{e^{ax+b}.dx}}$
$\mathcal{\frac{e^{ax+b}}{a}+c}$
10What is the solution to
$\mathcal{\int{\frac{1}{ax+b}.dx}}$
$\mathcal{\frac{1}{a}\ln{|ax+b|}+c}$
11Give the exponential expansion to
$\mathcal{\cosh{x}}$
$\mathcal{\frac{e^x+e^{-x}}{2}}$
12Give the exponential expansion to
$\mathcal{\sinh{x}}$
$\mathcal{\frac{e^x-e^{-x}}{2}}$
13Give the exponential expansion to
$\mathcal{\tanh{x}}$
$\mathcal{\frac{e^x-e^{-x}}{e^x+e^{-x}}}$