Limits

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

Find the equation from which to calculate the resistance of an infinite network of resistances.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.