Math H162    Brown    Wi04

Homework 7,  due Wednesday,  February 18,  2004

 

Problem  A.  Show that for any vector v,   v / | v | is a unit vector.

 

 

 

1.  Textbook, page  605:  #2a, 4, 6, 12

 

2.  Textbook, page 610-611:  #3, 4, 6, 8,

 

 

 

Problem B.  Get out your graphing calculator, or get together with a friend who has one.  Set the graphing window so that  x  goes from about  -20  to  +20  and  y  goes from about  -3  to  +3.

 

(a)  Graph the first term  x  of the Taylor series for  sin x,  and then superimpose on it the graph of  sin x.

 

(b)  Clear the window.  Now graph the Taylor series  for  sin x  out to the  cube term: 

 

x minus x3 / 3!.  Then superimpose on it the graph of  sin x.

 

(c)  Repeat  (b)  several times, increasing by one the number of nonzero terms of the Taylor series that you use.  See a pattern?

 

 

Problem  C.  (Extra credit)  Prove the triangle inequality for vectors.