Chapter 7.3, Problem 41E

To determine

To complete: The table of function, $y=\frac{x+4}{x^2-16}$ .

Answer to Problem 41E

  $\begin{array}{cc}x& y\\ -3.5& -0.133\\ -3.8& -0.128\\ -3.9& -0.126\\ -4.1& -0.123\\ -4.2& -0.122\end{array}$

Explanation of Solution

Given: $y=\frac{x+4}{x^2-16}$

The given function is, $y=\frac{x+4}{x^2-16}$ .

For $x=-3.5$ , $y=\frac{-3.5+4}{{\left(-3.5\right)}^2-16}=-0.133$

For $x=-3.8$ , $y=\frac{-3.8+4}{{\left(-3.8\right)}^2-16}=-0.128$

For $x=-3.9$ , $y=\frac{-3.9+4}{{\left(-3.9\right)}^2-16}=-0.126$

For $x=-4.1$ , $y=\frac{-4.1+4}{{\left(-4.1\right)}^2-16}=-0.123$

For $x=-4.2$ , $y=\frac{-4.2+4}{{\left(-4.2\right)}^2-16}=-0.122$

Now make table and complete it.

  $\begin{array}{cc}x& y\\ -3.5& -0.133\\ -3.8& -0.128\\ -3.9& -0.126\\ -4.1& -0.123\\ -4.2& -0.122\end{array}$

When trace the graph at $x=-4$ graph is undefined. Because it is hole of the rational function.

There exist limit but function is not continuous because $x=-4$ is hole of graph.