Problems of the day

1.

Get your turtle to draw something close to: (see solutions for the picture).

2.

Calculate the total length of the line segments making up the n'th tree ${\cal T}_n$ of section 4.4.

3.

Define a function f by

$$f : x \mapsto \sum_{k=0}^\infty \frac{cos(2^kx)}{{1.5}^k}.$$

Plot the graph of f from $-2\pi$ to $2\pi$ as well as you can. Compare this to the graph from -0.1 to 0.1. This function is continuous, but differentiable at no point. Can you prove this?

4.

Get Maple to draw something close to: (see solutions for the picture).