Explanation Given: The function is f ( x ) = e x ln x and the value of a and b is 1 and 1.02 respectively. Concept used: Linear approximation: For a differentiable function at x = a the linearization of a function f ( x ) is expressed as follows: f ( x ) ≈ f ( a ) + ( x − a ) f ′ ( a ) Calculation: The given function is expressed as follows: f ( x ) = e x ln x …..(1) Differentiate equation (1) as shown below: f ′ ( x ) = d ( e x ln x ) d x = e x x + e x ln x To obtain the value of f ′ ( 1 ) substitute 1 for x in the above equation as shown below: f ′ ( 1 ) = e 1 1 + e 1 ln 1 = e + 0 = e = 2.71828 To obtain the value of f ( 1 ) substitute 1 for x in equation (1) as shown below: f ( 1 ) = e 1 ⋅ ln 1 = e ⋅ 0 = 0 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: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 28E

To determine

To find:

The linearization of the function f(x)=exlnx at x=a and approximate the value of f(b) such that the value of a and b is 1 and 1.02 respectively.

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Chapter 4.1, Problem 27E

Chapter 4.1, Problem 29E

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Chapter 4 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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The linearization of the function f ( x ) = e x ln x at x = a and approximate the value of f ( b ) such that the value of a and b is 1 and 1.02 respectively.

Solution Summary: The author explains the linearization of the function f(x)=ex

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The linearization of the function f(x)=exlnx at x=a and approximate the value of f(b) such that the value of a and b is 1 and 1.02 respectively.

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The linearization of the function f ( x ) = e x ln x at x = a and approximate the value of f ( b ) such that the value of a and b is 1 and 1.02 respectively.

Solution Summary: The author explains the linearization of the function f(x)=ex

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To find: The linearization of the function f(x)=exlnx at x=a and approximate the value of f(b) such that the value of a and b is 1 and 1.02 respectively.

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Chapter 4 Solutions

To find:

The linearization of the function f(x)=exlnx at x=a and approximate the value of f(b) such that the value of a and b is 1 and 1.02 respectively.