Explanation Given: The functions f ( x ) = x 2 , f ( x ) = x , f ( x ) = x 3 . Formula used: δ f = f ( x + 1 ) − f ( x ) Square of sum formula: ( a + b ) 2 = a 2 + b 2 + 2 a b . Cube of sum formula: ( a + b ) 3 = a 3 + b 3 + 3 a b ( a + b ) Calculation: When f ( x ) = x 2 , we can write: ⇒ δ f = f ( x + 1 ) − f ( x ) ⇒ δ f = ( x + 1 ) 2 − x 2 ⇒ δ f = x 2 + 1 2 + 2 x − x 2 ⇒ δ f = 2 x + 1 When f ( x ) = x , we can write: ⇒ δ f

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 1.3, Problem 41E

To determine

To prove:

δf(x)=2x+1 if f(x)=x2.

To find:

Expressions for δf when f(x)=x and f(x)=x3.

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Chapter 1.3, Problem 40E

Chapter 1.3, Problem 42E

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Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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Prob. 43E Ch. 1.4 - Prob. 44E Ch. 1.4 - Prob. 45E Ch. 1.4 - Prob. 46E Ch. 1.4 - Prob. 47E Ch. 1.4 - Prob. 48E Ch. 1.4 - Prob. 49E Ch. 1.4 - Prob. 50E Ch. 1.4 - Prob. 51E Ch. 1.4 - Prob. 52E Ch. 1.4 - Prob. 53E Ch. 1.4 - Prob. 54E Ch. 1.4 - Prob. 55E Ch. 1.4 - Prob. 56E Ch. 1.4 - Prob. 57E Ch. 1.4 - Prob. 58E Ch. 1.4 - Prob. 59E Ch. 1.4 - Prob. 60E Ch. 1.4 - Prob. 61E Ch. 1.4 - Prob. 62E Ch. 1.4 - Prob. 63E Ch. 1.4 - Prob. 64E Ch. 1.4 - Prob. 65E Ch. 1.4 - Prob. 66E Ch. 1.5 - Prob. 1PQ Ch. 1.5 - Prob. 2PQ Ch. 1.5 - Prob. 3PQ Ch. 1.5 - Prob. 4PQ Ch. 1.5 - Prob. 1E Ch. 1.5 - Prob. 2E Ch. 1.5 - Prob. 3E Ch. 1.5 - Prob. 4E Ch. 1.5 - Prob. 5E Ch. 1.5 - Prob. 6E Ch. 1.5 - Prob. 7E Ch. 1.5 - Prob. 8E Ch. 1.5 - Prob. 9E Ch. 1.5 - Prob. 10E Ch. 1.5 - Prob. 11E Ch. 1.5 - Prob. 12E Ch. 1.5 - Prob. 13E Ch. 1.5 - Prob. 14E Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Prob. 17E Ch. 1.5 - Prob. 18E Ch. 1.5 - Prob. 19E Ch. 1.5 - Prob. 20E Ch. 1.5 - Prob. 21E Ch. 1.5 - Prob. 22E Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1 - Prob. 1CRE Ch. 1 - Prob. 2CRE Ch. 1 - Prob. 3CRE Ch. 1 - Prob. 4CRE Ch. 1 - Prob. 5CRE Ch. 1 - Prob. 6CRE Ch. 1 - Prob. 7CRE Ch. 1 - Prob. 8CRE Ch. 1 - Prob. 9CRE Ch. 1 - Prob. 10CRE Ch. 1 - Prob. 11CRE Ch. 1 - Prob. 12CRE Ch. 1 - Prob. 13CRE Ch. 1 - Prob. 14CRE Ch. 1 - Prob. 15CRE Ch. 1 - Prob. 16CRE Ch. 1 - Prob. 17CRE Ch. 1 - Prob. 18CRE Ch. 1 - Prob. 19CRE Ch. 1 - Prob. 20CRE Ch. 1 - Prob. 21CRE Ch. 1 - Prob. 22CRE Ch. 1 - Prob. 23CRE Ch. 1 - Prob. 24CRE Ch. 1 - Prob. 25CRE Ch. 1 - Prob. 26CRE Ch. 1 - Prob. 27CRE Ch. 1 - Prob. 28CRE Ch. 1 - Prob. 29CRE Ch. 1 - Prob. 30CRE Ch. 1 - Prob. 31CRE Ch. 1 - Prob. 32CRE Ch. 1 - Prob. 33CRE Ch. 1 - Prob. 34CRE Ch. 1 - Prob. 35CRE Ch. 1 - Prob. 36CRE Ch. 1 - Prob. 37CRE Ch. 1 - Prob. 38CRE Ch. 1 - Prob. 39CRE Ch. 1 - Prob. 40CRE Ch. 1 - Prob. 41CRE Ch. 1 - Prob. 42CRE Ch. 1 - Prob. 43CRE Ch. 1 - Prob. 44CRE Ch. 1 - Prob. 45CRE Ch. 1 - Prob. 46CRE Ch. 1 - Prob. 47CRE Ch. 1 - Prob. 48CRE Ch. 1 - Prob. 49CRE Ch. 1 - Prob. 50CRE

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To prove: δ f ( x ) = 2 x + 1 if f ( x ) = x 2 . To find: Expressions for δ f when f ( x ) = x and f ( x ) = x 3 .

Solution Summary: The author explains that delta f(x)=2x+1if

Videos

To prove:

δf(x)=2x+1 if f(x)=x2.

To find:

Expressions for δf when f(x)=x and f(x)=x3.

Want to see the full answer?

Chapter 1 Solutions

To prove: δ f ( x ) = 2 x + 1 if f ( x ) = x 2 . To find: Expressions for δ f when f ( x ) = x and f ( x ) = x 3 .

Solution Summary: The author explains that delta f(x)=2x+1if

Videos

To prove: δf(x)=2x+1 if f(x)=x2. To find: Expressions for δf when f(x)=x and f(x)=x3.

Want to see the full answer?

Chapter 1 Solutions

To prove:

δf(x)=2x+1 if f(x)=x2.

To find:

Expressions for δf when f(x)=x and f(x)=x3.