## Math 190 - Exam 1-2 Study Guide

1. Simplify the expression. Two parts. Look at problems 1.2.71 - 1.2.87
2. Rationalize the numerator. Look at problems 1.2.95 - 1.2.99.
3. Find the domain of the function. Two parts. Look at problems 2.1.17 - 2.1.29.
4. Find the rules for the composition of the functions: Two parts. Look at problems 2.2.25 - 2.2.29. Be careful to state restrictions when necessary. Be sure to include the absolute value if necessary.
5. Find the indicated one-sided limits, if they exist. Three parts. Look at 2.5.21 - 2.5.41
6. Find the slope of the tangent line to the graph at any point. Show Work. Two parts. Look at 2.6.9 - 2.6.15
7. Find the indicated limits, if they exist. Eight parts. Look at 2.4.17 - 2.4.61, 2.4.73 - 2.4.79
8. A graph is shown. Use the graph to find the value of a function at a specific point, estimate the average rate of change over an interval, estimate the instantaneous rate of change at a specific point, determine differentiability at a point, and state whether the function is continuous.
9. Find the values of x for which the function is continuous. Two parts. Look at 2.5.551 - 2.5.65

### Notes:

• None of the problems are directly from the text (unless I just happened to make up numbers that were in the book). Where problems to look at in the book are indicated, they are like problems in that section with the numbers changed.
 # 1 2 3 4 5 6 7 8 9 Total Pts 10 5 8 12 9 12 24 12 8 100