Explanation Given information: x + 3 = e x Calculation: Simplify the given equation. x + 3 = e x x + 3 − x + 3 = e x − x + 3 [ Subtract x + 3 from both sides ] 0 = e x − x + 3 Let f ( x ) = e x − x + 3 and the function f ( x ) has at least one real root on the interval (0, 1). So, find the value of function at x = 0 . f ( x ) = e x − x + 3 f ( 0 ) = e 0 − 0 + 3 f ( 0 ) = 1 − 3 f ( 0 ) < 0 And also, find the value of function at x = 1

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 82SP

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To prove that x+3=ex has at least one real root, and then use a graphing utility to find the root.

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Chapter 2, Problem 81SP

Chapter 2, Problem 83SP

Chapter 2 Solutions

Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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To prove that x + 3 = e x has at least one real root, and then use a graphing utility to find the root.

Solution Summary: The author explains how to find the root of sqrtx+3=ex using a graphing utility.

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To prove that x+3=ex has at least one real root, and then use a graphing utility to find the root.

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Chapter 2 Solutions