Explanation Given information: Given function is y = ( 1 + x ) − 1 2 , a = 3 Formula used: For a function f ( x ) , the linearization at x = a is: L ( x ) = f ′ ( a ) ( x − a ) + f ( a ) Calculation: The function is y = ( 1 + x ) − 1 2 . Write the function as y = f ( x ) . f ( x ) = ( 1 + x ) − 1 2 Differentiate the above function. f ′ ( x ) = − 1 2 ( 1 + x ) − 3 2 For x = a , write the function f ( x ) = ( 1 + x ) − 1 2 as: f ( a ) = ( 1 + a ) − 1 2 Substitute 3 for a . f ( 3 ) = ( 1 + 3 ) − 1 2 = ( 4 ) − 1 2 = 1 2 Write the function f ′ ( x ) = − 1 2 ( 1 + x ) − 3 2 as: f ′ ( a ) = − 1 2 ( 1 + a ) − 3 2 Substitute 3 for a

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.1, Problem 50E

To determine

To calculate:

The linearization of the given function at x=a.

y=(1+x)−12,a=3

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Chapter 4.1, Problem 49E

Chapter 4.1, Problem 51E

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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The linearization of the given function at x = a . y = ( 1 + x ) − 1 2 , a = 3

Solution Summary: The author explains how to calculate the linearization of the given function at x=a.

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To calculate:

The linearization of the given function at x=a.

y=(1+x)−12,a=3

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Chapter 4 Solutions

The linearization of the given function at x = a . y = ( 1 + x ) − 1 2 , a = 3

Solution Summary: The author explains how to calculate the linearization of the given function at x=a.

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To calculate: The linearization of the given function at x=a. y=(1+x)−12,a=3

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Chapter 4 Solutions

To calculate:

The linearization of the given function at x=a.

y=(1+x)−12,a=3