Courses   <-  Sean Forman   <-  You Are Here Applied Calculus I

September 19 or 20, 2005

First Exam Review. The first exam is Friday, September 23, 2005.

You will not need a special calculator, one able to do basic arithmetric will be sufficient. Any calculator capable of doing symbolic differentiation will not be allowed (for example the TI-89 and above). You will not have any notes or formulas available to you. Here is a summary of topics covered in the first part of the course. There may be other topics not listed here. You are responsible for all material covered in class and on homework.

The solutions to all assigned homework problems will be available on reserve in the library on Monday afternoon. Go to the front desk and ask for the homework solutions to Dr. Forman's Math 1351 class. The exam will be designed so that you should be able to complete it in 50 minutes.

1. Section 2.1 Understanding how the secant line can approach the tangent line. Using calculations to estimate the derivative.

2. Section 2.2 Limits calculated numerically, understanding some pitfalls of using calculations, one-sided limits, infinite limits, vertical asymptotes.

3. Section 2.3 Limit laws, need to be able to use them, but not memorized (1, 2, 6, etc.) Need to understand when we can do direct substitution. How the overall limit and one-sided limits are related. squeeze theorem.

4. Section 2.4 Precise definition of a limit. Should be able to do a linear equation using the precise definition. Know the precise definition. I may give you $\delta =$ some function of $\epsilon$ and ask you to complete the proof. The better you understand the idea of a limit the better off you will be. Really think about what these values mean.

5. Section 2.5 Continuity. Definition of continuity, continuous on an interval, types of functions and where they are continuous. Intermediate value theorem.

6. Section 2.6 Horizontal asymptotes. Limit as $x \to \infty$. How to calculate these by factoring and by algebra.

7. Section 2.7 Tangents and rates of change.

8. Section 2.8 Finding derivatives and rates of change using the definition of the derivative. Calculating values. Understanding and writing in full sentences what the derivative means and what different values stand for. What the units are.

9. Section 2.9 Being able to sketch the graph of $f'(x)$ when shown $f(x)$. Calculating $f'(x)$ using the definition of the derivative for various functions.

The exam is not yet completed, but I anticipate the test looking very similar to the homework problems. There may be a couple of extra questions that aren't homework questions, but knowing how to do all of the homework will prepare you very well. Obviously, you should also read through the text and notes as well.