Interesting Questions

For graph sketching questions, see here.

If you have an interesting question which you would like to be featured in this bank, please email it to me using the contact form.

Question: A curve is given parametrically by `x=frac{9t}{1+t^3}` and `y=frac{9t^2}{1+t^3}`. Sketch the curve and comment on the behaviour as \(t \to -1\).

Problem: Prove \(n^{(n-1)!}\)  divides  \((n!)!\)  (i.e. that \((n!)!\) is a multiple of \(n^{(n-1)!}\)).

Problem: Evaluate \(\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}\) . Now evaluate \(\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+\cdots}}}}\)  and  \(\sqrt{n-\sqrt{n-\sqrt{n-\sqrt{n-\cdots}}}}\)  for  \(n>0\).