Math 190 - Final Exam Study Guide

1. Find the indicated limits. Eight parts.
2. Evaluate the limits by making a table of values. Two parts.
3. Use the table to find the indicated derivatives. Seven parts. A table of x, f(x), g(x), f'(x), and g'(x) values are given. You're then asked to evaluate the derivatives of sums, differences, products, constant multiples, and compositions of functions. As an example. If f(1)=2, g(1)=3, f'(3)=2 and g'(1)=3, the [f(g(1))]' = f'(g(1)) * g'(1) = f'(3)*g'(1) = 2 * 3 = 6.
4. Find the derivative of the function. Twelve parts.
5. Evaluate the integral. Ten parts. Some are indefinite, some are definite. Some require u-substitutions (including the fun kind), Some are improper.
6. Use integration by parts to evaluate the definite integral.
7. Use implicit differentiation to find dy/dx.
8. Use the definite integrals given to find other definite integrals. Three parts. As an example, if the "definite integral from 2 to 4 of f(x) is 6" and the "definite integral from 4 to 7 of f(x) is 8", find the "definite integral from 2 to 7 of f(x)". The answer, of course, is 6 + 8 = 14.
9. Find the first order partial derivatives.
10. Find the second derivatives. Two parts.
11. Find the area of the region between two curves.
12. Sketch a function with the given characteristics.
13. Consider a polynomial function. Find the intervals where the function is increasing, decreasing, concave up, and concave down. Find any relative extrema and inflection points.
14. Find the absolute maximum and minimum of a function on a closed interval.
15. Use Simpson's Rule to approximate the area under a curve on a given interval. Use the numerical integration capabilities of the calculator to find the actual value. Find the relative error in Simpson's approximation. Relative Error = (estimate - actual) / actual.

Notes:

• Most of the problems were obtained by looking at previous tests and arriving at similar problems. None of the problems are directly from previous tests. None of the problems are knowingly from the textbook.
• You may use your notebooks on the test. The notebook may contain notes, homework, old tests, study guides, and any handouts. It may not contain photocopies of the text, nor may the text be three-hole punched and stuck into your notebook.