MATH 255A, Review for Midterm Test 2

Test topics

1. Continuity of functions. Basic types of discontinuities: jumps, asymptotes, gaps. Piecewise defined functions (3.2)
2. Limits of functions. Left and right limits, two-sided limits. Limits at infinity (3.1)
3. Average rate of change. Instantaneous rate of change. The derivative (3.3, 3.4)
4. Finding the derivative using the definition (3.4)
5. Geometrical interpretation of the derivative. Equation of the tangent line. Increasing and decreasing functions and the derivative. Examples when the derivative does not exist (3.4).
6. Basic rules for finding derivatives (sums, differences, constant multiple, power rule) (4.1)
7. Product and quotient rules (4.2)
8. The chain rule (4.3)
9. Exponential and logarithmic functions (4.4, 4.5)

Formulas/facts you need to know for the test

• Different notations for the derivative (4.1)
• All the formulas in blue boxes in 4.1, 4.2, 4.3, except the one on p. 227 (we did not discuss it in class, and it is a consequence of the chain rule).
• The formula for the derivative of e^mx (the particular case of the blue box for e^g(x) with g(x)=mx)
• The blue box on p. 224 and the derivative for ln |x| from the blue box on p. 245
• Equation for the tangent line (blue box on p. 183)

Preparation for the test

Problems on the test will not be taken from the homework/practice problems but they will be generally similar. The best way to prepare is to study examples in the lectures and in the book and to solve practice problems (think about how to solve it, rather than look in the answer). To get the idea of the time, you may try to solve these in one hour:

3.1: 53, 79, 3.2: 23, 3.R: 17, 35, 3.4: 17, 4.1: 59; 4.2: 45, 4.R: 27, 33.

General rules

Tests are closed books/notes. Simple scientific calculator (example: TI-30XII) is allowed on the test. Graphing calculators (example: TI-83, 84, 89) cannot be used. Calulator is not required to answer the questions. You should justify all answers properly. Partial credit will be given depending on how well you explain your solutions. Correct answers without explanations will receive zero points.