BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.5, Problem 23E
To determine

To show: For f(x)=5x the equality f(x+h)f(x)h=5x(5h1h) holds..

Expert Solution

Explanation of Solution

Results used:

Law of exponent:

If a and b are positive numbers and x  and y are any real numbers, then bx+y=bxby .

Calculation:

If f(x)=5x , then. f(x+h)=5x+h .

Therefore, by using law of exponents,

f(x+h)f(x)h=5x+h5xh=5x5h5xh=5x(5h1)h

Thus, for f(x)=5x equation f(x+h)f(x)h=5x(5h1h) holds.

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