The following is a chapter by chapter guide intended to help you organize the material we have covered in class as you study for your exam. It is only intended to serve as a guidline, and may not explicitly mention everything that you need to study. This exam is cumulative, so it is important that you remember the material from earlier chapters as well. It is also still important that you are comfortable with the basics of differention and integration (as covered in Calculus I).
Please review all homework, quiz and workshop problems for the chapters given below, and make sure you can solve all of them. You can also look at these problems for additional practice for each chapter.
11.1: Look over all the examples from Section 11.1 and make sure you can under- stand all the steps, especially for the ones involving finding a parametrization for a given curve. You should also know how to eliminate the parameter, and how to find tangent lines without eliminating the parameter.
11.2 & 8.1: Practice applying the arc length and surface area formulas by solving problems from both of these sections. Also know how to find the speed of a particle whose motion is given by parametric equations. Note that trig integrals and trig substitutions are often needed to solve the integrals that come up in these sections.
11.3 & 12.7: You should understand how to identify points in terms of polar co-ordinates, and how to go back and forth between polar and rectangular co-ordinates. You should know how to plot the graphs for two-dimensional functions in polar form, especially for the examples given in chapter 11.3.
11.4:Know how to find area and arc length in terms of polar co-ordinates. Practice applying these formulas, especially finding the correct limits of integration. Note that trig integrals often arise in problems relating to these sections.
9.1:You should know what it means for a differential equation to be separable, and how to solve it in this case. You should also understand what initial conditions are and how to use them.
9.2:You should be able to apply the methods of Section 9.1 to solve differential equations of the form y' = k (y - b) and use the result to solve problems similar to the homework problems for this section.
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