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.