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Chapter 7: Problem 25

Use the limit definition to find the derivative of the function. $$ f(x)=3 $$

Short Answer

Expert verified
The derivative of the function \(f(x)=3\) is \(0\).

Step by step solution

01

Write down the function

Our function is simply \(f(x) = 3\), a horizontal line at \(y = 3\).
02

Write down the limit definition of the derivative

The limit definition of the derivative, also known as the formal definition or the difference quotient, is: \[f'(x) = \lim_{h\rightarrow0} [f(x+h)-f(x)]/h\]
03

Substitute the function into the limit definition

Using \(f(x) = 3\), the limit definition becomes: \[f'(x) = \lim_{h\rightarrow0} [(3)-(3)]/h = \lim_{h\rightarrow0} [0]/h\]
04

Evaluate the limit

As \(h\) approaches zero, \(0/h\) is always \(0\). Therefore the limit is \(0\).

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Most popular questions from this chapter

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ s(t)=\frac{1}{t^{2}+3 t-1} $$

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