Readings Questions:

You should read the section before attempting any reading questions or problems. Remember that you are responsible for all definitions and examples. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.

1)   Use definition 3.5.1 to verify that   for .   Hint:  Recall that for  to be a linear transformation there is a scalar m such that .  Then equation (3.5.1) becomes

2)   Look in your  Calculus I book and state Taylor's theorem for a function .  Compare this to the linear approximation on page 193 and the differential approximation (3.5.9) on page 195.

3)   Look in your  Calculus I book and state the chain rule.  Also present a proof of the chain rule.
 
 

Problems:

page  197     1, 2, 5, 7, 11, 13, 16, 17, 20, 21, 25, 27, 31, 39, 40
 

page  208     1, 3, 6, 9, 10, 13, 17, 19, 24, 27, 31, 35, 38, 43