Chapter 11, Problem 13RE

Solution

To find: The value of the limit $\underset{x\to \infty }{{\displaystyle \lim }}\frac{2-x^2}{x}$ and use the table to justify the value.

The value of the limit $\underset{x\to \infty }{{\displaystyle \lim }}\frac{2-x^2}{x}$ is $-\infty$ .

Given information:

The given limit is $\underset{x\to \infty }{{\displaystyle \lim }}\frac{2-x^2}{x}$ .

Calculation:

When $x$ approaches $\infty$ , the denominator will be very small. So, the value will be undefined.

Substitute the limit and simplify.

  $\begin{array}{c}\underset{x\to \infty }{{\displaystyle \lim }}\frac{x\left(\frac{2}{x}-x\right)}{x}=\underset{x\to \infty }{{\displaystyle \lim }}\left(\frac{2}{x}-x\right)\\ =\left(\frac{2}{\infty }-\infty \right)=-\infty \end{array}$

Use graphical calculator to find the values in the tabular form as given below.

  

Therefore, the required value is undefined.