Math 250 Final Exam Review Sheet

Sections Covered:

• 4.4 (L'Hospital's Rule)
• 7.1-7.5 & 7.8 (Integration)
• 8.1-2 (arc length & surface area)
• 10.1-10.5 (parametric equations & polar coordinates)
• 11.1-11.11 (sequences & series)

Review worksheets: Prof. Zeman has written a series of worksheets. These would be very good for you to review. See Worksheets

Formulas to know:

• You should know the formulas & graphs on the 2 pages inside the front cover of your book. [Maybe not the one for tan(2x).] Also, know and be able to use the trig identies on page 481 [2].
• There are four pages of formulas at the back of your book:
• You should know the DIFFERENTIATION RULES 1-21. (Note that this includes the first three inverse trig functions.)
• In the TABLE OF INTEGRALS (three pages) you should
  • Know 1-18, be be able to derive 19 & 20.
  • Recognize that 21-62 can be derived, for the most part, by trig-substitutions.
  • Be able to derive 63-86 by various trig identities and integration by parts.
  • Be able to derive 87-95 by integration by parts.
  • Same for 96-102. (100 you should know.)
  • Skip 103-112.
  • Recognize that 113-120 can be derived, for the most part, by completing the square and then applying a trig-substitution.
• The arc length formulas in triangular coordinates (page 542-543 [2],[3], & [4]), for parametric equations (page 656 [4]), and in polar coordinates (page 673 [5]).
• The surface area formulas in rectangular coordinates (pages 549-550, [4]-[6]), and in polar coordinates (658, [5]).
• Area in a polar region (page 671, [3] or [4]), including between polar curves.
• The Geometric Series formula/convergence test (page 706 [4]).
• Of course all the convergence tests and methods.
• Be able to make error estimates using the Alternating Series Estimation Theorem (page 729) and the Remainder Estimate for the Integral Test (page 718, [2]).
• The Taylor and Maclaurin series definitions (page 752, [5]-[6]).
• The series in the box on page 758.
• The binomial series (page 763, [2]).

The best way to study is to work lots and lots of problems. Do not spend too much time sitting around memorizing formulas. The formulas will come to feel natural if you use them to solve problems.

GOOD LUCK!!