Explanation Given: The function is f ( x ) = e x and the value of a and b is 1 and 0.85 respectively. Concept used: Linear approximation: For a differentiable function at x = a the linearization is expressed as follows: f ( x ) ≈ f ( a ) + ( x − a ) f ′ ( a ) Calculation: The given function is expressed as follows: f ( x ) = e x …..(1) Differentiate equation (1) as shown below: f ′ ( x ) = d ( e x ) d x = e x ⋅ 1 2 x = e x 2 x To obtain the value of f ′ ( 1 ) substitute 1 for x in the above equation as shown below: f ′ ( 1 ) = e 1 2 ⋅ 1 = e 2 = 2.71828 2 = 1.85914 To obtain the value of f ( 1 ) substitute 1 for x in equation (1) as shown below: f ( 1 ) = e 1 = 2.71828 The expression to obtain the linear approximation of a function is as follows: L ( x ) = f ( a ) + ( x − a ) f ′ ( a ) Substitute 1 for a in the above equation

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 4.1, Problem 27E

To determine

To find:

The linearization of the function f(x)=ex at x=a and approximate the value of f(b) such that the value of a and b is 1 and 0.85 respectively.

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Chapter 4.1, Problem 26E

Chapter 4.1, Problem 28E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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The linearization of the function f ( x ) = e x at x = a and approximate the value of f ( b ) such that the value of a and b is 1 and 0.85 respectively.

Solution Summary: The author explains the linearization of the function f(x)=esqrtx at x=a and the approximated value of

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The linearization of the function f(x)=ex at x=a and approximate the value of f(b) such that the value of a and b is 1 and 0.85 respectively.

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The linearization of the function f ( x ) = e x at x = a and approximate the value of f ( b ) such that the value of a and b is 1 and 0.85 respectively.

Solution Summary: The author explains the linearization of the function f(x)=esqrtx at x=a and the approximated value of

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To find: The linearization of the function f(x)=ex at x=a and approximate the value of f(b) such that the value of a and b is 1 and 0.85 respectively.

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Chapter 4 Solutions

To find:

The linearization of the function f(x)=ex at x=a and approximate the value of f(b) such that the value of a and b is 1 and 0.85 respectively.