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Chapter 14: Q. 44 (page 889)

In Problems 33-44, find the one-sided limit.
$\lim_{x \to - 4^{-}} \frac{x^{2} + x - 12}{x^{2} + 4 x}$

Short Answer

Expert verified

The value is $\frac{7}{4}$

Step by step solution

01

Given information

Given function $\lim_{x \to - 4^{-}} \frac{x^{2} + x - 12}{x^{2} + 4 x}$

02

Sketching the graph

The graph is

03

Checking the limit

Checking, we get

For $x \to 4 -$ , $x$ is close to four but less than $4$ so

$\lim_{x \to - 4^{-}} (\frac{x^{2} + x - 12}{x^{2} + 4 x}) = \frac{7}{4}$

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Most popular questions from this chapter

Use a graphing utility to find the indicated limit rounded to two decimal places.

$\lim_{x \to 1} \frac{x^{3} - x^{2} + 3 x - 3}{x^{2} + 3 x - 4}$

True or False Every polynomial function has a graph that can be traced without lifting pencil from paper.

In Problems 7– 42, find each limit algebraically.

$\lim_{x \to 2} {(3 x - 2)}^{5 / 2}$ .

True or False The exponential function $f (x) = e^{x}$ is increasing on the interval $(- \infty, \infty)$ . (p. 280)

In Problems 13–32, use the accompanying graph of y = f(x).

Find $\lim_{x \to - 6^{-}} f (x) .$

See all solutions

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