Explanation Given: The functions f and g . Formula used: δ f = f ( x + 1 ) − f ( x ) Calculation: We can write: ⇒ δ f = f ( x + 1 ) − f ( x ) ⇒ δ g = g ( x + 1 ) − g ( x ) Now, applying first difference on sum of the two functions, we get: ⇒ δ ( f + g ) = ( f + g ) ( x + 1 ) − ( f + g ) ( x ) ⇒ δ ( f + g ) = f ( x + 1 ) + g ( x + 1 ) − ( f ( x ) + g ( x ) ) ⇒ δ ( f + g ) = f ( x + 1 ) + g ( x</

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.3, Problem 43E

To determine

To prove:

For two functions, f and g, δ(f+g)=δf+δg and δ(cf)=cδf.

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Chapter 1.3, Problem 42E

Chapter 1.3, Problem 44E

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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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