Math 120-03 Fall 1999 Study Guide for Test #1 Take-home test

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• Covers HWKs 3-10 plus some of HWKs 1-2
• Handed out Monday October 18 & due Wednesday 20th
• Closed-book but use handout "Frequently Used Maclaurin Series"
• To be written in one sitting of at most 90 minutes
• Topics and/or techniques covered
  Basic integration techniques, including u-substitution, integration by parts, and partial-fractions for nonrepeated linear factors
  May include double-back integration by parts
  Basic material on limits and continuity, including one-sided limits, infinite limits, and limits for x tending to infinity, definition of continuity
  Indeterminate forms and l'Hospital's rule, including "e it up'
  Comparing relative rates of growth of functions
  Improper integrals, including definition of convergence/divergence for improper integrals
  Introductory material on series: definition/formula for Taylor and Maclaurin polynomials and series, operations on series such as algebra, substitution, differentiation, integration (all done with an ``18th-century attitude'' that assumes such operations are meaningful/legitimate0
  Finding limits for indeterminate forms by using series
  Not included: trigonometric substitution
  Not included: formal definitions for limit statements, squeeze theorem
  Not included: comparison test for improper integrals
  
• Sections covered
  1.2 Rules for Finding Limits
  1.4 Extensions of the Limit Concept
  1.5 Continuity
  3.5 Limits as x --> +/- infinity, Asymptotes, and Dominant Terms (but not oblique asymptotes)
  4.3 Integration by Substitution--Running the Chain Rule Backward
  4.8 Substitution in Definite Integrals
  6.6 L'Hospital's Rule
  6.7 Relative Rates of Growth (but not big-Oh, little-oh notation)
  7.2 Integration by Parts
  7.3 Partial Fractions (for nonrepeated linear factors)
  7.6 Improper Integrals
  8.9 Taylor and Maclaurin Series
  8.11 Applications of Power Series (Examples 5,7,8,9 and related problems only)
  
• Additional Review Problems
  Chapter 1 Practice Exercises p104: 1, 3, 5,13, 15, 17
  Chapter 2 Practice Exercises p181: 65ab, 67ab, 95, 99, 103, 107 (ok to use l'H on these)
  Chapter 3 Practice Exercises p269: 53, 55
  Chapter 4 Practice Exercises p357: 31, 33, 39, 43, 53, 67
  Chapter 6 Practice Exercises p548: 89, 91, 93, 95, 97bd
  Chapter 7 Practice Exercises p606: 19, 25, 83, 85, 89, 91, 99, 113, 115, 117
  Chapter 8 Practice Exercises p700: 53, 57 (two ways), 63 (two ways), 65, 67, 81a
  
• Practice Test available in class Monday Oct 18
  The practice test should give you a reasonable indication of roughly what kind of exam and what kind of problems to expect.

Questions?
Come to my office or send me e-mail or post on the FirstClass Q&A conference for the course As always, to ask about a particular problem from the text, please give page or section number, give problem number, and make your question as specific as you can.

• Alexia Sontag, Mathematics
• Created by: Kate Golder
• Wellesley College
• Date Created: June 28, 1999
• Last Modified: October 17, 1999
• Expires: August 31, 2000