Calculus of a Single Variable: Early Transcendental by Professor Ron Larson, Bruce H Edwards

By Professor Ron Larson, Bruce H Edwards

The one Variable part of Calculus: Early Transcendental services, 5/e, deals scholars leading edge studying assets. each version from the 1st to the 5th of Calculus: Early Transcendental features, 5/e has made the mastery of conventional calculus talents a concern, whereas embracing the easiest positive aspects of latest expertise and, whilst acceptable, calculus reform rules.

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Additional info for Calculus of a Single Variable: Early Transcendental Functions, 5th Edition

Example text

For instance, the function given by f ͑x͒ ϭ 2x 2 Ϫ 4x ϩ 1 can be described by the form f ͑᭿͒ ϭ 2͑᭿͒ Ϫ 4͑᭿͒ ϩ 1 2 where parentheses are used instead of x. To evaluate f ͑Ϫ2͒, simply place Ϫ2 in each set of parentheses. f ͑Ϫ2͒ ϭ 2͑Ϫ2͒2 Ϫ 4͑Ϫ2͒ ϩ 1 ϭ 2͑4͒ ϩ 8 ϩ 1 ϭ 17 Substitute Ϫ2 for x. Simplify. Simplify. NOTE Although f is often used as a convenient function name and x as the independent variable, you can use other symbols. For instance, the following equations all define the same function. f ͑x͒ ϭ x 2 Ϫ 4x ϩ 7 Function name is f, independent variable is x.

If b2 Ϫ 4ac > 0 and a has two x-intercepts. 0, then the graph of y ϭ ax 2 ϩ bx ϩ c 86. If b 2 Ϫ 4ac ϭ 0 and a 0, then the graph of y ϭ ax 2 ϩ bx ϩ c has only one x-intercept. 29x. 37, 5 Յ x Յ 100 x2 In Exercises 87 and 88, find an equation of the graph that consists of all points ͧx, yͨ having the given distance from the origin. ) 87. The distance from the origin is twice the distance from ͑0, 3͒. 88. The distance from the origin is K ͑K from ͑2, 0͒. 2 Preparation for Calculus Linear Models and Rates of Change ■ ■ ■ ■ ■ Find the slope of a line passing through two points.

Y ϭ 1 2x In Exercises 15 and 16, describe the viewing window that yields the figure. 15. y ϭ x3 ϩ 4x 2 Ϫ3 ԽԽ Խ Խ 16. y ϭ x ϩ x Ϫ 16 x3 ϩ2 3 42. y ϭ Ϫ 2x ϩ 6 2 44. y ϭ 3 x ϩ 1 51. y ϭ xΊx ϩ 5 52. y ϭ Ί25 Ϫ x2 53. x ϭ y3 54. x ϭ y 2 Ϫ 4 55. y ϭ 8 x 56. y ϭ ԽԽ 57. y ϭ 6 Ϫ x 10 x2 ϩ 1 Խ Խ 58. y ϭ 6 Ϫ x In Exercises 59–62, use a graphing utility to graph the equation. Identify any intercepts and test for symmetry. In Exercises 17 and 18, use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places.

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