Explanation Given: The function is f ( x ) = e x and the value of a and b are 0 and − 0.1 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 ) Error: The formula to calculate the error is as follows: Error = | Δ f − f ′ ( a ) Δ x | Calculation: The given function is expressed as follow: f ( x ) = e x ….(1) The expression Δ f represents the change is the value of f ( x ) as the value of value of x is changed from a to b . The value of Δ f is calculated as follows: Δ f = f ( b ) − f ( a ) = f ( − 0.1 ) − f ( 0 ) Label the above equation as equation (2). Δ f = f ( − 0.1 ) − f ( 0 ) …..(2) Substitute 0 for x in equation (1) as shown below: f ( 0 ) = e 0 = 1 Substitute − 0.1 for x in equation (1) as shown below: f ( − 0.1 ) = e − 0.1 = 1 e 0.1 = 0.9048 To obtain the value of Δ f substitute the value of f ( 0 ) and f ( − 0.1 ) in equation (2) as shown below: Δ f = 0.9048 − 1 = − 0.0952 Differentiate equation (1) with respect to x as shown below: f ′ ( x ) = d ( e x ) d x = e x Substitute 0 for x in the above equation as shown below: f ′ ( 0 ) = e 0 = 1 The value of Δ x is calculated as follows: Δ x = − 0

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 19E

To determine

To find:

The value of Δf, error and the value of f(b) for the function f(x)=ex such that the value of a and b is 0 and −0.1 respectively.

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Chapter 4.1, Problem 18E

Chapter 4.1, Problem 20E

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CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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The value of Δ f , error and the value of f ( b ) for the function f ( x ) = e x such that the value of a and b is 0 and − 0.1 respectively.

Solution Summary: The author explains the value of Delta f, error, and the linear approximation of the given function, L(x)=1+x.

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To find:

The value of Δf, error and the value of f(b) for the function f(x)=ex such that the value of a and b is 0 and −0.1 respectively.

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Chapter 4 Solutions

The value of Δ f , error and the value of f ( b ) for the function f ( x ) = e x such that the value of a and b is 0 and − 0.1 respectively.

Solution Summary: The author explains the value of Delta f, error, and the linear approximation of the given function, L(x)=1+x.

Videos

To find: The value of Δf, error and the value of f(b) for the function f(x)=ex such that the value of a and b is 0 and −0.1 respectively.

Want to see the full answer?

Chapter 4 Solutions

To find:

The value of Δf, error and the value of f(b) for the function f(x)=ex such that the value of a and b is 0 and −0.1 respectively.