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Chapter 2 Review Calculus Slide 2 Quick Review 1.) f(2) = 0 2.) f(2) = 11/12 3.) f(2) = 0 4.) f(2) = 1/3 Slide 3 Slide 2- 3 Quick Review (-4, 4) (-1, 5) Slide 4 Slide 2- 4 Example Limits Remember to always try to plug in what you are approaching, if you get a value then that is your limit. Slide 5 Slide 2- 5 Example Limits Slide 6 [-6,6] by [-10,10] by graphing: Slide 7 Slide 2- 7 Example One-Sided and Two-Sided Limits o 12 3 4 Find the following limits from the given graph. Slide 8 Slide 2- 8 Quick Review Solutions [-12,12] by [-8,8][-6,6] by [-4,4] Slide 9 Slide 2- 9 Quick Review Solutions Slide 10 Slide 2- 10 [-6,6] by [-5,5] Example Horizontal Asymptote Slide 11 Slide 2- 11 Example Sandwich Theorem Revisited Slide 12 Example Vertical Asymptote [-6,6] by [-6,6] Slide 13 Example Seeing Limits as x Slide 14 Slide 2- 14 Quick Quiz Sections 2.1 and 2.2 Slide 15 Slide 2- 15 Quick Quiz Sections 2.1 and 2.2 Slide 16 Slide 2- 16 Quick Quiz Sections 2.1 and 2.2 Slide 17 Slide 2- 17 Quick Review Solutions Slide 18 Slide 2- 18 Quick Review Solutions Slide 19 Slide 2- 19 Quick Review Solutions Slide 20 Slide 2- 20 Quick Review Solutions Slide 21 Slide 2- 21 Example Continuity at a Point o Slide 22 Slide 2- 22 Continuity at a Point x = 0 Continuous Removable DiscontinuityRemovable Jump Dis. Infinite Dis. Oscillating functions are not continuous, infinite discontinuity Slide 23 Example Continuity at a Point [-5,5] by [-5,10] Slide 24 Slide 2- 24 Continuous Functions [-5,5] by [-5,10] Slide 25 Quick Review Solutions Slide 26 Slide 2- 26 Quick Review Solutions Slide 27 Slide 2- 27 Quick Review Solutions Slide 28 Slide 2- 28 Average Rates of Change The average rate of change of a quantity over a period of time is the amount of change divided by the time it takes. In general, the average rate of change of a function over an interval is the amount of change divided by the length of the interval. Also, the average rate of change can be thought of as the slope of a secant line to a curve. Slide 29 Slide 2- 29 Example Average Rates of Change Slide 30 Example Tangent to a Curve Slide 31 Slide 32 Slide 2- 32 Slope of a Curve Slide 33 Slide 2- 33 Slope of a Curve at a Point Slide 34 Slide 2- 34 Normal to a Curve The normal line to a curve at a point is the line perpendicular to the tangent at the point. The slope of the normal line is the negative reciprocal of the slope of the tangent line. Slide 35 Slide 2- 35 Example Normal to a Curve Slide 36 Slide 2- 36 Quick Quiz Sections 2.3 and 2.4 Slide 37 Slide 2- 37 Quick Quiz Sections 2.3 and 2.4 Slide 38 Slide 2- 38 Quick Quiz Sections 2.3 and 2.4 Slide 39 Chapter Test Solutions Slide 40 Slide 2- 40 Chapter Test Solutions Slide 41 Slide 42 Slide 2- 42 Chapter Test Slide 43 Slide 2- 43 Chapter Test Solutions Slide 44 Slide 2- 44 Chapter Test Solutions