MA 126
Review for Final Exam
Spring 2015
The exam is on Wednesday, May 6, 10:30–12:30. Material covered: Sections 5.3–5.6; 7.1; 6.1–6.5; 8.1–8.4
and 8.7; chapter 9 (except binomial series); 10.1–10.5.
Start your review from the beginning. Make sure you think about the progression of ideas, not just individual
definitions and formulas. Now is the time to put what you have learned in perspective and remind yourself
how it all hangs together. Use the review sheets for the first three exams as a guide. In addition:
Parametric curves: Be able to parameterize simple curves such as line segments, circles, and graphs of
functions. Know how to eliminate the parameter to get a Cartesian equation, sketch the portion of the curve
traced for the given parameters and show the direction of motion. (It is NOT always appropriate to solve
for t. The goal is to get a simple equation that you know how to graph. Thus x = cos t, y = sin t should be
rewritten as x2 + y 2 = 1, not y = sin(cos−1 t), which is nasty and does not give you the entire circle.)
Know how to find the slope of a tangent to a parameterized curve. Know how to find arc length and area of
a surface of revolution. (The formulas are the same as the ones in chapter 6, but with arc length differential
p
ds = (dx/dt)2 + (dy/dt)2 dt.)
Polar coordinates: Be able to convert coordinates, and simple equations, from Cartesian to polar form
and polar to Cartesian. Know how to find all polar representations of a given point. Be able to graph polar
functions r = f (θ) similar to the ones encountered in class and on homework, and find the slope of a tangent
line. Know how to find areas of polar regions. (You don’t need to learn the polar arc length formula. Two
versions is enough for one exam.)