Math 242, Fall 2013, Assignment 7

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.

- Goethe

Carefully define the following terms:

1. Differentiable (function).
2. Linearization (of a differentiable function).
3. Tangent plane (to the graph of a differentiable function).
4. Increment (of an input variable).
5. Differential (of an input variable).
6. Increment (of an output variable).
7. Differential (of an output variable).

Carefully state the following theorems:

1. Formula for the linearization of a differentiable function (equation 3 on page 772).
2. Formula for the total differential (equation 10 on page 774).
3. Sufficient condition for differentiability (Theorem 8 on page 773).
4. The Chain Rule.
5. Formula for implicit partial differentiation (equation 7 on page 786).

Solve the following problems:

1. Section 11.4, problems 5, 11, 15, 23, and 33.
2. Section 11.5, problems 1, 11, 13, 21, 27, 29 and 33.

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