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Chapter 14: Q. 22 (page 906)

Find $\lim_{x \to - 4^{+}} f (x)$ .

Short Answer

Expert verified

The limit $\lim_{x \to - 4^{+}} f (x)$ is $- 2$ .

Step by step solution

01

Step 1. Graph the function f(x)

We have been given $\lim_{x \to - 4^{+}} f (x)$ .

Now let us graph the function with the help of a graphing utility.

02

Step 2. Finding the limit from the graph.

In the graph, consider the behavior of $f (x)$ near $x = - 4$ when approaching from the right side.

The real value of $f (- 4) = 1$ .

However coming from the right side, the value of the function approaches $- 2$ .

That is $\lim_{x \to - 4^{+}} f (x) = - 2$ .

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Most popular questions from this chapter

In Problems 7– 42, find each limit algebraically.

$\lim_{x \to 2} {(3 x - 4)}^{2}$

In Problems 43-52, find the limit as $x$ approaches $c$ of the average rate of change of each function from $c$ to $x$ .

$c = 1; f (x) = \frac{1}{x}$

Graph each function. Use the graph to find the indicated limit, if it exists.

$\lim_{x \to \frac{π}{2}} f (x), f (x) = \sin (x)$

True or False The limit of a rational function at $5$ equals the value of the rational function at $5$

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x \to 0}{l i m} f (x), f (x) = \{\begin{cases} e^{x} & i f x > 0 \\ 1 - x & i f x \leq 0 \end{cases}$

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