MATH 550
Professor Girardi
Quiz 3
Due Thursday 10 February 2000 by 3pm for everyone.

  1. Problem 7e from Chapter 2 Review (pg 165).
    Your solution should be of the form: ax + by + cz = d .
    Remark: similar to homework problem 7c from Chapter 2 Review.
  2. Problem 8c from Chapter 2 Review (pg 165).
    Your solution should be of the form: ax + by + cz = d .
    Remark: similar to homework problem 8b from Chapter 2 Review.
  3. Problem 22 from Chapter 2 Review (pg 167).
    Remark: this is one of the homework problems.
  4. Problem 16 from section 2.6 (pg 153).
    1. hint: 2nd to last line on page 9 of Informal Summary
    2. hint: the last line on page 9 of Informal Summary
    3. directional derivative and ideas from direction angles in action .

Comments that should help with problems 3 and 4.

For problem 16 from section 2.6:
Let u be a unit vector in R3. Then the directional derivative of T at (1,1,1) in the direction of u, i.e.
Du   T (1,1,1)
is the rate of change of T at (1,1,1) in the direction of u, where the units of this rate of change is in
degrees per meter.
So if Captain Ralph is at (1,1,1) and heads off in the direction of u with a speed of e8 meters per second, the ship's hull temperature is changing at a rate of:
{Du   T (1,1,1) } times {e8}     degrees per second.

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