### MATH 9B  --  Midterm #2 Review Topics

Section Topics
5.1, 5.2 Refer to the list of review topics from our previous exam.

5.3 Arc length formula for the graph of a function y(x).
Arc length formula for parametric (plane) curves.
Exercises 3-6, 9, any of 11-16.

5.4 Pumping liquids from containers.
Examples 6, 7.
Exercises 17-19, 35.

5.5 Fluid force against a vertical plate.
Examples 2, 3.
Exercises 1, 2, 5, 6, 11.

5.6 Moment M0 , mass M , and center of mass M0 / M
of a strip along an axis with given density function.
Examples 1, 2.
Exercises 1, any of 5-12.

6.1 The natural logarithm, its domain, range, and derivative.
Laws of logarithms.
Logarithmic differentiation.
Logarithms with general bases (other than e).
Exercises Any of 1-66.

6.2 The derivative rule for inverse functions.
Inverse equations for ex and ln(x).
Definition of e as a limit.
General exponential functions (with bases other than e),
their derivatives and anti-derivatives.
Exercises 15-18, 41-44, 45-50, 51-58.

6.3 Derivatives of the inverse trigonometric functions.
Examples 7-9.
Exercises 1, 2, 7-10, 13, 14, 18, 19, 21-26, 27-30.

6.7 Definitions of odd and even functions.
Definitions of the basic hyperbolic functions.
Derivatives of sinh, cosh, and tanh.
Closed formulas for sinh-1, cosh-1, and tanh-1.
Exercises 5-10, 61-63.

7.1 As discussed in class on Friday, 11/18/2005.

Disclaimer: No claim is being made that this list of review topics/exercises is necessarily extensive.