Chapter 11.2, Problem 59E

a.

To determine

To graphically approximate the limit $\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}$ by using a graphing utility to graph the function.

Answer to Problem 59E

  $-0.125$

Explanation of Solution

Given:

  $\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}$

Graph:

  

b.

To determine

To numerically approximate the limit $\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}$ using graphing utility.

Answer to Problem 59E

  $-0.125$

Explanation of Solution

Calculation:

Make a table for the function $y=\frac{4-\sqrt{x}}{x-16}$.

x	15.9	15.99	15.999	16	16.1	16.01	16.001
y	-0.125110	-0.125020	-0.125003	-0.125000	-0.124806	0.124980	0.124998

c.

To determine

To evaluate the limit of the function $\frac{4-\sqrt{x}}{x-16}$ as $x\to {16}^{+}$ .

Answer to Problem 59E

  $-0.125$

Explanation of Solution

Given:

  $\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}$

Calculation:

Firstly, simplify the function by rationalising then substituting value of limit.

  $\begin{array}{l}\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}\\ =\underset{x\to {16}^{+}}{\lim }\frac{4-\sqrt{x}}{x-16}\times \frac{4+\sqrt{x}}{4+\sqrt{x}}\\ =\underset{x\to {16}^{+}}{\lim }\frac{{(4)}^2-{(\sqrt{x})}^2}{(x-16)(4+\sqrt{x})}\\ =\underset{x\to {16}^{+}}{\lim }\frac{-(x-16)}{(x-16)(4+\sqrt{x})}\\ =\underset{x\to {16}^{+}}{\lim }\frac{-1}{(4+\sqrt{x})}\\ =\frac{-1}{(4+\sqrt{16})}\\ =\frac{-1}{8}\\ =-0.125\end{array}$