Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

Two shops each have different numbers of jumper designs and colours. How many choices of jumper are there?

Use the quotient rule to differentiate various functions.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

Write complex numbers in real-imaginary form.

Poles, residues, and contour integral of a complex-valued function.  Pair of pure imaginary poles.

Poles, residues, and contour integral of a complex-valued function.  Pair of real poles.

Poles, residues, and contour integral of a complex-valued function.  Single, simple pole.

Contour integral of $z^2$ along any path.

Contour integral of $\mathrm{e}^{-z}$ along any path.

Contour integral of a complex-valued function $f(z)$ with the poles of $f(z)$ either inside or outside the path $C$.

Given a payoff table with two states and five actions, identify which actions are admissible, then the maximax, maximin, and minimax regret actions.

Given a payoff table with two states and five actions, identify which actions are admissible, then the maximax, maximin, and minimax regret actions.

Should state that input is by integers or fractions. Also  the maximax, maximin and minimax regret actions are not asked for.

Given a payoff table with two states and five actions, identify which actions are admissible, then the maximax, maximin, and minimax regret actions.

Given a payoff table with two states and five actions, identify which actions dominate others, and identify admissible actions.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$.

Given $f(x)=(x+b)^n$. Find the gradient and equation of the chord between $(a,f(a))$ and $(a+h,f(a+h))$ for randomised values of $a$, $b$ and $h$.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Modulus and argument of a single complex number, where $\mathrm{Re}(z)=\mathrm{Im}(z)$.

Polar form of a complex number.

Calculate the principal value of a complex number.