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Big, Bigger, Biggest

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

Complex Sine

Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.

Gosh Cosh

Age 16 to 18 Challenge Level:
To sketch the graphs, consider whether the functions are odd or even and consider values of the functions for $x=0$ and for very large $x$. Confirm your sketch by differentiating the functions and finding the turning points.

To prove the hyperbolic trig identities requires only some simple algebra.