Homework 4

# Homework 4 - APPM 2350 HOMEWORK 04 Due by 4 PM on Friday...

This preview shows pages 1–2. Sign up to view the full content.

APPM 2350 HOMEWORK 04 FALL 2010 Due by 4 PM on Friday, September, 24, 2010 in your TA’s mailbox 1. Work all of the “suggested” textbook problems. Remember that you do not need to write them up or submit them. Just be sure you can do, and understand, all of them prior to starting the homework problems that you submit for grading. 2. If you have not ±nished problem 1, go back and ±nish it. 3. Suppose that a smooth curve r ( t ) has the parameterization r ( t )=( x ( t ) ,y ( t )) for t R . We will assume that this parameterization is in terms of arclength. For a given point t 0 R ,w e de±ne the function K ( t ) as K ( t )= N ( t 0 ) · ( r ( t 0 ) r ( t )) | r ( t 0 ) r ( t ) | 2 . Clearly, K ( t ) is continuous when t ° = t 0 . Our goal is to investigate the continuity of K ( t )when t = t 0 . a. Show that for the parameterization given above, we can write the curvature κ ( t ) as κ ( t )= | x ° ( t ) y °° ( t ) y ° ( t ) x °° ( t ) | ( x ° ( t ) 2 + y ° ( t ) 2 ) 3 / 2 . b. Letting θ equal the angle between N ( t 0 ) and r ( t ) r ( t 0 ), show that we can simplify K ( t )to K ( t )= cos( θ ) | r ( t 0 ) r ( t ) |

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Homework 4 - APPM 2350 HOMEWORK 04 Due by 4 PM on Friday...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online