Chapter 3.2, Problem 10QR

To determine

To calculate: The value of the given function $f\left(x\right)$ .

Answer to Problem 10QR

The required value $f\left(x\right)$ of the line is $5$ .

Explanation of Solution

Given information:

If $f\left(x\right)=5x$ then find the value $\frac{f\left(3+0.001\right)-f\left(3-0.001\right)}{0.002}$

Formula used; Distributive property formula:.

  $a\left(b+c\right)=ab+ac$ .

Calculation:

The given function is:

  $f\left(x\right)=5x$

Find the value of $\frac{f\left(3+0.001\right)-f\left(3-0.001\right)}{0.002}$ bysubstitute of given function. and use distributive property.

Now,

  $\frac{f\left(3+0.001\right)-f\left(3-0.001\right)}{0.002}$

Substitute the given function $f\left(x\right)=5x$ in the above expression.

  $\begin{array}{c}\frac{f\left(3+0.001\right)-f\left(3-0.001\right)}{0.002}=\frac{5\left(3+0.001\right)-5\left(3-0.001\right)}{0.002}\\ =\frac{5\left(3.001\right)-5\left(2.999\right)}{0.002}\\ =\frac{5\left(3.001-2.999\right)}{0.002}\\ =\frac{5\left(0.002\right)}{0.002}\\ =5\end{array}$

Hence, the required value of $f\left(x\right)$ is $5$ .