By Ron Larson, Bruce H. Edwards
The Larson CALCULUS software has a protracted background of innovation within the calculus industry. it's been greatly praised by way of a new release of scholars and professors for its sturdy and powerful pedagogy that addresses the desires of a large variety of educating and studying types and environments. each one identify is only one part in a entire calculus direction software that conscientiously integrates and coordinates print, media, and know-how items for profitable instructing and studying.
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Additional resources for Calculus (9th Edition)
B) Complete the graph of f given that f is odd. (b) The thermostat is reprogrammed to produce a temperature H͑t͒ ϭ T͑t Ϫ 1͒. How does this change the temperature? Explain. (c) The thermostat is reprogrammed to produce a temperature H͑t͒ ϭ T͑t͒ Ϫ 1. How does this change the temperature? Explain. CAPSTONE 88. Water runs into a vase of height 30 centimeters at a constant rate. The vase is full after 5 seconds. Use this information and the shape of the vase shown to answer the questions if d is the depth of the water in centimeters and t is the time in seconds (see figure).
G Њ f Solution a. ͑ f Њ g͒͑x͒ ϭ f ͑g͑x͒͒ ϭ f ͑cos x͒ ϭ 2͑cos x͒ Ϫ 3 ϭ 2 cos x Ϫ 3 b. ͑g Њ f ͒͑x͒ ϭ g ͑ f ͑x͒͒ ϭ g͑2x Ϫ 3͒ ϭ cos͑2x Ϫ 3͒ Note that ͑ f Њ g͒͑x͒ ͑ g Њ f ͒͑x͒. Definition of f Њ g Substitute cos x for g͑x͒. Definition of f ͑x͒ Simplify. Definition of g Њ f Substitute 2x Ϫ 3 for f ͑x͒. Definition of g͑x͒ ■ 26 Chapter P Preparation for Calculus EXPLORATION Use a graphing utility to graph each function. Determine whether the function is even, odd, or neither. f ͑x͒ ϭ x 2 Ϫ x 4 g͑x͒ ϭ 2x 3 ϩ 1 h ͑x͒ ϭ x 5 Ϫ 2x 3 ϩ x TEST FOR EVEN AND ODD FUNCTIONS j ͑x͒ ϭ 2 Ϫ x 6 Ϫ x 8 k ͑x͒ ϭ x 5 Ϫ 2x 4 ϩ x Ϫ 2 p ͑x͒ ϭ x9 ϩ 3x 5 Ϫ x3 ϩx Describe a way to identify a function as odd or even by inspecting the equation.
35. ͑0, 0͒, ͑4, 8͒ 36. ͑0, 0͒, ͑Ϫ1, 5͒ 37. ͑2, 1͒, ͑0,Ϫ3͒ 38. ͑Ϫ2, Ϫ2͒, ͑1, 7͒ 39. ͑2, 8͒, ͑5, 0͒ 40. ͑Ϫ3, 6͒, ͑1, 2͒ 41. ͑6, 3͒, ͑6, 8͒ 42. ͑1, Ϫ2͒, ͑3, Ϫ2͒ 43. ͑ ͒, ͑0, ͒ 1 7 2, 2 3 4 44. ͑ ͒, ͑ 7 3 8, 4 5 4, Ϫ 14 ͒ 45. Find an equation of the vertical line with x-intercept at 3. 46. Show that the line with intercepts ͑a, 0͒ and ͑0, b͒ has the following equation. y x ϩ ϭ 1, a a b 0, b 0 47. x-intercept: ͑2, 0͒ 2 48. x-intercept: ͑Ϫ 3, 0͒ y-intercept: ͑0, Ϫ2͒ y-intercept: ͑0, 3͒ 49. Point on line: ͑1, 2͒ 50.
Calculus (9th Edition) by Ron Larson, Bruce H. Edwards