Lecture 13: Composition of Functions

Problem of the day 5

This problem is due on test day, September 25. The temperature at a point (x,y) in the plane is given by P(x,y)= x²+y²-4x+2y.
Find the coldest point in the plane and the temperature at that point.

Assignments

These are the problems you should work before today, February 5.
Review problems, page 75, 4n+1, for n=0..22;
Section 1.1, page 92, 4n+1, for n=0...24;
Section 1.2, page 102, 1-6, and 4n, for n=3...23;
Section 1.3, page 113, 4n+1, for n=0...19.

These are the problems you should work before February 12.
Section 1.4, page 120, problems 6n+1, for n=0...15;
(skip 1.5) 1.6, page 149, problems 6n+1, for n=0...16.

These are the problems you should work before February 19.
Section 1.7, page 160, 4n+1, for n=0,...,24.
Section 1.8, page 171, problems 6n+1, for n=0...8;

These are the problems you should work before February 26.
The first test, covering Chapters P and 1 and sections 2.1 and 2.2 is on February 26.
Section 2.1, page 191, problems 6n+1, for n=0...12.
Section 2.2, page 025, problems 8n+1, for n=0...11.
Test 1 with answers
Test 2 with answers
Test 3 with answers

Brief review of the lecture

We talked about the three methods of representing (discussing) functions:
the symbolic form, using an equation,
the tabular form with a list of x-values and their corresponding y-values, and
the graphical form. It is absolutely essential that you be able to convert from one of these forms to the others. In particular, for example if f(2)=4, then the value in the y column whose row has the x value 2 is 4. Look carefully at problems 2 and 3 on Test 2 with answers
Be sure you understand how to work these problems.

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