Math 242, Spring 2019, Assignment 6

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

- Goethe

Read:

1. Section 14.2.
2. Section 14.3.

Carefully define the following terms, then give one example and one non-example of each:

1. Limit (of $f(x,y)$, as $(x,y)$ approaches $(a,b)$) (this is Definition 1 on page 904).
2. Continuous (function of several variables, at a given point).
3. Partial derivative (of a function $f$, with respect to a given variable).

Carefully state the following theorems (you do not need to prove them):

1. Clairaut's Theorem.

Solve the following problems:

1. Section 14.2, problems 5, 7, 9, 17, 18, 19, 29, 31, 33, and 35.
2. Section 14.3, problems 1, 3, 5, 10, 15, 17, 19, 21, 29, 33, 53, and 59.

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