**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**