Math 122: Chapter 7 Study Guide

1. Find a formula for the derivative of the inverse of a function. Look at problems 7.3.7-10.
2. Solve the logarithmic or exponential equation for x. Two parts. Look at problems 7.1.16-33.
3. Find the derivative of one of the inverse trigonometric functions by using an appropriate triangle and the derivative of a trigonometric function. Look at pages 490-493 and your lecture notes.
4. Find the derivatives. Eight parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
5. Find the derivative of an integral using the second part of the fundmental theorem of calculus. Look at problems 7.6.15-22.
6. Use logarithmic differentiation to find the derivative. Look at problems 7.2.31-34
7. Use calculus to find the coordinates of the absolute maximum and minimum of the continuous function on the closed interval. Remember from Calculus 1 that absolute extrema can occur at critical points or at end points. Look at problems 7.4.5-8.
8. Integrate. Give exact answers when there are definite integrals. Six parts. These could include logarithmic, exponential, inverse trigonometric, hyperbolic trigonometric, or inverse hyperbolic trigonometric functions.
9. Find the limit. Six parts. Look at problems 7.5.5-34.

Notes

• Show work!
• You may create notecards that have the following formulas on them.
  • Integrals resulting in an inverse trigonometric function (page 494)
  • Derivatives of the inverse hyperbolic trigonometric functions (page 505)
  • Integrals resulting in an inverse hyperbolic trigonometric function (page 506). Do not use the equivalent logarithmic form.
• You are expected to know the derivatives of the inverse trigonometric functions.
• You are expected to know the derivatives of the trigonometric and hyperbolic trigonometric functions.

Points per problem

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Last updated August 31, 2006 9:33 AM