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finalstudyguide

# finalstudyguide - mean being able to identify the pattern...

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Final Exam Study Guide Approximately forty percent of the exam will cover the material from the first midterm. Particularly important topics include the following: Computing Derivatives and Integrals from Their Definitions Numerical Integration with the Trapezoid Rule Integration to Find the Area Between Two Curves Integration to Find Volume Trigonometric Methods of Integration The various integration methods, for example integration by substitution, in- tegration by parts, and improper integration, will be required in the problems dealing with area and volume, as well as in problems about the later material. The next forty percent of the exam will cover the material from the second midterm. Particularly important topics include the following: All of the Tests for Series Convergence Writing a Repeating Decimal as a Rational Number Convergence or Divergence of a Sequence from the Definition Finding the Domain of a Power Series Taylor Polynomials and Taylor Series You’ll want to be able to write the Taylor series of a given function, which will
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Unformatted text preview: mean being able to identify the pattern established by taking repeated deriva-tives and substituting that into the general formula for the coeﬃcents. Good practice problems are Section 8.8 #17, 21, 25, 28, 29. The remaining twenty or so percent of the exam will cover functions of multiple variables. Topics to review include the following: Level Curves: Discussion on pp. 974-975 Section G1.1 #15, 17, 23, 24, 25, 26 Partial Diﬀerentiation: Discussion on pp. 978-985 Section G1.2 #1, 3, 5, 7, 9, 11, 19 Maxima and Minima of Functions of Two Variables: Discussion on pp. 987-992, especially First Derivative Test on p. 989 and the Second Derivative Test on p. 992 Example 4 on p. 992 Section G1.3 #1, 3, 5, 11, 13, 17, 19, 21 You’ll be given the formula sheet from the ﬁrst exam plus the formula for D ( x, y ) in the statement of the Second Derivative Test for functions of two variables....
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