# Homework Assignment 8

Assigned Tuesday October 29; due Friday November 8, 2PM at SS 1071

this document in PDF: HW08.pdf

All of Spivak Chapter 9.

## To be handed in

From Spivak Chapter 9: 1, 9, 15, 23.

## Recommended for extra practice

From Spivak Chapter 9: 8, 11, 21, 28.

Also, let be the polynomial . Now that we know that for we have that

complete the proof of the following

Theorem.

• If is odd then the equation has a root for any value of .
• If is even then there is some constant so that the equation has no roots for , has at least one root for and at least two roots for .

## Just for fun

Write a computer program that will allow you to draw the graph of the function

and will allow you to zoom on that graph through various small windows''. Use your program to convince yourself that is everywhere continuous but nowhere differentiable. The best plots will be posted on this web site! (Send pictures along with window coordinates by email to drorbn@math.toronto.edu).

The generation of this document was assisted by LATEX2HTML.

Dror Bar-Natan 2002-10-28