List of Important Exercises

Transcription

1 List of Important Exercises This is a running list of the standard problems from each section. Although all exercises in the book, believe it or not, are relevant to building a complete understanding of that section s topic, the problems below are the most crucial these are the ones that you definitely would need to be able to do before moving on. Sec. 4.5 Solve an indefinite integral using substitution: #5 26, and Solve a definite integral using substitution: #55 62 and Apply even and odd symmetry to definite integrals: #69 76 Sec. 4.6: Approximation using trapezoid rule or Simpson s rule: #1 10 (Section 4.6 is conceptually important. If you need to prioritize though, you don t need to know this section for later sections.) Sec. 5.1: Differentiate a function involving ln x: #41 64 Use logarithmic differentiation: #89 94 (Review implicit differentiation as needed: #73 76) (Review log properties as needed: #1 40) Sec. 5.2: Solve integrals involving ln x: #1 30, and (Read Example 9 on the trick for integrating sec x) (Review FTC II as needed: #63 66) Sec. 5.3: Find the derivative of an inverse at a point: #63 70 (Review deciding if f is invertible and finding f 1 if possible: #1 46) Sec. 5.4: Differentiation involving e x : #33 52, Integration involving e x : # (Review solving equations algebraically as needed: #1 16) 1

2 Sec. 5.5: Differentiation involving b x or log b x: #37 66 Integration involving b x : #71 82 (Review solving equations algebraically as needed: #19 34) Sec. 5.6: Differentiate using inverse trig: #39 58, Evaluate inverse trig expressions using a right triangle: #25 32 (Review evaluating trig/inverse trig as needed: #3 10, 33 36) Sec. 5.7: Integration with inverse trig: #1 46, Sec. 7.1: Find the area of a region between two curves, including sketching the curves or possibly integrating with respect to y instead of x: #1 30, Sec. 7.2: Find the volume of a solid of revolution by the disk method, including revolution about an arbitrary vertical or horizontal axis: #1 36 Find the volume of a solid whose cross sections are other basic geometric shapes: #71 72 Good challenging practice: #55 62 Sec. 7.3: Find the volume of a solid of revolution by the shell method, including revolution about an arbitrary vertical or horizontal axis: #1 32 Sec. 7.4: Find the arc length of part of a graph: #3 16 Find the surface area of a solid of revolution, including about a vertical axis: #37 42 and

3 Sec. 7.5: This section applies the techniques developed in Chapter 7. There s not a new technique critical to later sections Calculate the work done by a varying force: Hooke s Law: #5 10 Propulsion: #11 14 Pumping water: #15 24 Lifting a chain: #25 30 Sec. 8.1 (review; not covered in class): Solve mixed indefinite integrals: #5 46 (important) Solve mixed definite integrals: #57 68 (important) Sec. 8.2: Use integration by parts to solve integrals: #11 30, 39 48, Sec. 8.3: Use trig identities to help solve integrals: #1 12, 19 32, Sec. 8.4: Use trig substitution to solve integrals: #21 46 Sec. 8.5: Use partial fractions to solve integrals: #5 26 Combine partial fractions with other techniques to solve integrals: #27 34 Sec. 8.8: Evaluating improper integrals to ± : #17 32 Evaluating improper integrals involving an asymptote: #33 48 (Useful but not essential yet) Predict if an improper integral converges by inspection: #53-62 Sec. 9.1: Basics of sequences (as needed): #1 20 Important: Determine convergence/divergence of a sequence: #

4 Sec. 9.2: Determine convergence/divergence of a series: #41 54, Sec. 9.3: Using the integral test: #1 22 Recognizing p-series: #33 38 Important: Mixed convergence/divergence of a series: #47 52, Sec. 9.4: Using direct comparison test: #3 12 Using limit comparison test: #13 22 Important: Mixed convergence/divergence of a series: #23 30 Sec. 9.5: Using the alternating series test: #5 26 Use the remainder theorem for alternating series: #31 36 Absolute vs conditional convergence: #37 54 Important: Mixed convergence/divergence of a series: #71 80 Sec. 9.6: Using the ratio test: #13 34 Using the root test: #35 50 Important: Mixed convergence/divergence of a series: #51 68, Important: The chart on p. 632 summarizes sections Sec. 9.7: Finding a Maclaurin/Taylor polynomial: #13 30 Sec. 9.8: Find the radius/interval of convergence: #5 34 Reindex a series (practice as needed): #41 44 Differentiating/integrating a series: #45 48 Sec. 9.9: Find a power series using the geometric formula: #5 16,

5 Evaluate a series by recognizing a geometric power series: #49 54, Sec. 9.10: Find a Taylor series using the definition: #1 12 Use known Taylor series to derive new ones: #17 44, Sec. 6.3: Use separation of variables to solve a differential equation: #1 28 Sec. 6.4: Use integrating factors to solve a differential equation: #5 24 5