MATH 390 Final Exam Name____________

Instructions: Answer all the questions on the paper provided.

I. Identifications. (5 points each)

Briefly identify each of the following:

1. Al-Khwarizmi

2. The Binomial Series

3. Girolamo Cardano

4. Georg Cantor

5. Indivisible

II. Answer each of the following questions with a few complete sentences. (7 each)

1. What problem brought about the need for the new definitions of the concepts of Calculus produced by Cauchy?

2. What did Abel prove concerning the solution of polynomial equations in one variable?

3. Why are Newton and Leibniz given credit as the discoverers (or inventors) of Calculus?

III. Problems

1. Which two of the following numbers are not be prime and explain how this can be determined from the form of the numbers? (10)

2. Find three possible factors (greater than 1) of 2¹⁰¹-1 and indicate how you know these are possible factors. (9)

3. Find the following binomial coefficient: (5)

=

4. Simplify . (8)

5. Find the slope of the tangent line to at (4,4) using Descartes’ circle method. (12)

6. Find one root of x³ + 6x² = 32 using Cardano’s formula. You may leave the answer in radical form. Cardano’s formulas are listed below: (10)

For ,