FinalExamPrep

# FinalExamPrep - Problems 8.8 57-59 55 37 8(6 Applications...

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MATH 31B (TOPICS FOR REVIEW) (1) Exponential and logarithmic functions (their properties; derivatives; loga- rithmic differentiation) (see chapter 7). Problems: 7.2: 26, 36. 7.3: 9, 12, 43, 44, 34, 36, 38. 7.4: 38, 24, 39, 40, 49. (2) Inverse trigonometric functions (their definitions; properties; derivatives) (section 7.5). Problems: 7.5: 7, 9, 10, 12, 14, 21, 31, 36. (3) L’Hospital rule. Problems: 7.7: 10, 12, 30, 47-50, 57-62. (4) Techniques of integration (integration by parts; substitutions; integration of trigonometric functions; trigonometric substitutions; integration of rational functions). Suggestion: section 8.5 is very useful in helping you to figure out what techniques of integration to choose in a particular example. Problems: 8.5: 1, 5, 11, 19, 23, 14, 18, 20, 24, 27, 33, 41, 42, 44, 55, 65, 62, 64, 78. (5) Improper integrals.
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Unformatted text preview: Problems: 8.8: 57-59, 55, 37, 8. (6) Applications of integration (arc length and area of surface of revolution). Problems: 9.1: 17-20; 9.2: 10, 12, 14, 16. (7) Sequences (convergence; monotonic sequence theorem). Problems: Chapter 12 review (p. 823): 1-9. (8) Series (de±nition of convergence; partial sums; geometric series; harmonic series; p-series; integral test; estimates of sum; comparison test; limit com-parison test; alternating series test; absolute convergence; ratio and root test). Problems: Chapter 12 review (p. 823): 11, 13, 15, 19, 20, 22, 23, 26, 35, 32, 36. (9) Power series (de±nition; representation of functions as power series; Taylor and MacLaurin series). Problems: Chapter 12 review (p. 823): 34, 45, 46, 47, 49, 51, 55, 62. 1...
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