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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 44 (page 889)

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

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

Sketching the graph

The graph is

03

Checking the limit

Checking, we get

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

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

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