Magnitude of Quantities and De L'Hospital's Rule

A. Magnitude of Quantities

The following quantities are arranged in the order of their rate of rise for large x [Here is a positive number less than 1.]

To ascertain their behavior for small y make the substitution .

The following approximations hold for small x.

Theorem 1

If as , and

Example 1.

Example:

Exercise 1.

Problem: Find

Exercise 2.

Problem: Give an approximate expression for for small r.