hoh Math 125 Section 02 Fall 2008

# Math 125 Section 02 Fall 2008

## Midterm solutions

### Lecture of October 31

Our book does not define a monotonically increasing and decreasing function very well (see page 4).

A function f is increasing if the values of f(x) increase as x increases.
A function f is decreasing if the values of f(x) decrease as x increases.
It is not clear, for instance, whether a constant function is increasing.

The Wikipedia entry for increasing function is a conventional way to resolve any ambiguity.

For instance, according to the Wikipedia definition, a constant function is both monotonically increasing and monotonically decreasing, but not strictly monotonically increasing or strictly monotonically decreasing.

The definition of monotonicity in our book appears to be equivalent (given the interpretation above!) to the definition of strict monotonicity

### Lecture of November 3

The details of the two examples done in class are here

### De L'Hopital Rule and Mean Value Theorems

These are supplementary notes focused on the math involved in the De L'Hopital Rule.

### What if a quantity is proportional to two other quantities?

This is a comment in regard to one homework problem about illumination. The statement "Illumination is proportional to the cosine of an angle and inversely proportional to the square of the distance from the light source" results in the formula

I = k * cos(theta) / r2