Chapter 8.3, Problem 5E

Solution

To identify: The step-by-step manual by using a spreadsheet to explore the difference between $f\left(x\right)\text{ and }g\left(x\right)$ as value of x increases. The given functions are $f\left(x\right)=\frac{12x^2-7}{3x}\text{ and }g\left(x\right)=4x$

The difference between $f\left(x\right),g\left(x\right)$ becoming lesser as $\left|x\right|$ increases to larger values.

Given information:

The given functions are $f\left(x\right)=\frac{12x^2-7}{3x}\text{ and }g\left(x\right)=4x$

Explanation:

Consider the given functions.

Write the value of given function in spreadsheet:

  

Enter the value of x as shown:

  

Write the formula:

Formula for $f\left(x\right)$ in cell B2 is (12(A2)^2-7)/(3*A2+4).

Formula for $g\left(x\right)$ in cell C2 is 4*A2.

Formula for $f\left(x\right)-g\left(x\right)$ in cell D2 is B2-C2.

Fill the formulas in B2, C2 and D2.

Move the cursor to the bottom left of these cells until the plus sign appeals and draw the mouse to the last row.

  

The difference between $f\left(x\right),g\left(x\right)$ becoming lesser as $\left|x\right|$ increases to larger values.

Hence, $g\left(x\right)$ is a oblique asymptote to $f\left(x\right)$ .