Explanation Calculation: Algebraic solution: Consider the equation, e − 2 x − 2 x e − 2 x = 0 . The equation can be rewritten as, 1 − 2 x e − 2 x = 0 ….. (1) Separate the above equation into two parts for two solutions: For 1 − 2 x = 0 : 1 − 2 x = 0 2 x = 1 Add 1 on both sides x = 1 2 Divide by 2 on both sides Also from equation (1): e − 2 x = 0 This doesn’t give any solution as e − 2 x ≠ 0 . Therefore, the only possible solutions of the equation e − 2 x − 2 x e − 2 x = 0 is x = 1 2 . Graphical solution: Consider the equation, e − 2 x − 2 x e − 2 x = 0 . Rewrite the equation as: e − 2 x = 2 x e − 2 x Take y 1 = e − 2 x and y 2 = 2 x e − 2 x . Plot the graph of y 1 = e − 2 x and y 2 = 2 x e − 2 x on the same set of axis The point of intersection of the graphs y 1 = e − 2 x and y 2 = 2 x e − 2 x gives the solution of the equation, e − 2 x − 2 x e − 2 x = 0

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 5.4, Problem 76E

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To calculate: The solution of the equation e−2x−2xe−2x=0 algebraically, and approximate the result to three decimal places. Also, verify the result graphically using graphing utility.

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Chapter 5.4, Problem 75E

Chapter 5.4, Problem 77E

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Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Evaluating an Exponential Function In Exercises...Ch. 5.1 - Evaluating an Exponential Function In Exercises...Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Graphing an Exponential Function Exercises 1724,...Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Transformations of the Graph of an Exponential...Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - 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The solution of the equation e − 2 x − 2 x e − 2 x = 0 algebraically, and approximate the result to three decimal places. Also, verify the result graphically using graphing utility.

Solution Summary: The author explains how to calculate the solution of the equation e-2x2, and verify the result graphically using graphing utility.

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To calculate: The solution of the equation e−2x−2xe−2x=0 algebraically, and approximate the result to three decimal places. Also, verify the result graphically using graphing utility.

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Chapter 5 Solutions