Solve for $x$: $a\cosh(x)+b\sinh(x)=c$. There are two solutions for this example.

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

Find  $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Differentiate the function $(a + b x)^m  e ^ {n x}$ using the product rule.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.

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. 8 paired observations.

Spearman rank correlation calculated. 10 paired observations.

Express $\displaystyle \frac{a}{x + b} +\frac{cx+d}{(x + b)^2}$ as an algebraic single fraction.

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

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Questions which try to emphasise that f(x) does not mean f times x.

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.