Homework Assignment 8
Assigned Tuesday October 29; due Friday November 8, 2PM at SS 1071
All of Spivak Chapter 9.
From Spivak Chapter 9: 1, 9, 15, 23.
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
- 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 .
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
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