Explanation Given: The given equation is e − x 2 = x Concept Used: The Intermediate Value Theorem: If f is continuous on the closed interval [ a , b ] and let N be any number between f ( a ) and f ( b ) , where f ( a ) ≠ f ( b ) . Then there exists a number c in ( a , b ) such that f ( c ) = N . Calculation: To show that there is a root of the equation e − x 2 = x in interval ( 0 , 1 ) First let f ( x ) = e − x 2 − x = 0 and a = 0 , b = 1

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 2, Problem 34E

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To show that there is a root of the equation:

e−x2=x , in interval (0,1) , using the Intermediate Value Theorem

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Chapter 2, Problem 33E

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Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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

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To show that there is a root of the equation: e − x 2 = x , in interval ( 0 , 1 ) , using the Intermediate Value Theorem

Solution Summary: The author calculates the root of the equation e-x2=x using the Intermediate Value Theorem.

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To show that there is a root of the equation:

e−x2=x , in interval (0,1) , using the Intermediate Value Theorem

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Chapter 2 Solutions

To show that there is a root of the equation: e − x 2 = x , in interval ( 0 , 1 ) , using the Intermediate Value Theorem

Solution Summary: The author calculates the root of the equation e-x2=x using the Intermediate Value Theorem.

Concept explainers

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To show that there is a root of the equation: e−x2=x , in interval (0,1) , using the Intermediate Value Theorem

Want to see the full answer?

Chapter 2 Solutions

To show that there is a root of the equation:

e−x2=x , in interval (0,1) , using the Intermediate Value Theorem