Math 180 F
Fall 2009
Exam 2 Review
Disclaimer: I have attempted to be comprehensive in the following, but important items may have been omitted by mistake. If you see such an omission, please let me know, but you are responsible for all of the lecture material to
the point covered in this exam..
The second hour exam for Math 180 will be held on Friday, October 23, and will cover section 2.3 through section 3.5 of the textbook. In particular, be prepared to:
- Be able to give a formal definition of a limit and demonstrate how one can find an appropriate δ for a given ε (for a simple function).
- Be able to find infinite limits and to identify asymptotes
(all three kinds) and give (rough) sketches of graphs of functions.
- Define continuity and identify points at which functions may not be continuous.
- Know the basic properties of continuous functions, including the intermediate value theorem (and its applications).
- Know the definition of a derivative, and be able to find (simple) derivatives using the definition. Know the relationships between derivatives and tangent lines.
- Know the rules for calculating derivatives: In particular be able to calculate the derivatives of polynomial, rational, exponential and trigonometric functions, and products and quotients of functions.
- Be able to construct tangent lines to points of a curve.
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Be able to take the derivatives of trigonometric, exponential, logarithmic
functions.
- Be able to apply the chain rule in simple cases (as in Assignment #7)
- Derivatives of inverse trig functions will not be on this exam.
Any questions? Please ask!