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Chapter 14: Q. 43 (page 889)

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

Short Answer

Expert verified

The value is $\frac{3}{2}$

Step by step solution

01

Given information

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

02

Sketching the graph

The graph is

03

Checking the limit

For $x \to - 2 +$ , $x$ is close to $- 2$ but greater than $- 2$ so

$\lim_{x \to - 2^{+}} (\frac{x^{2} + x - 2}{x^{2} + 2 x}) = \frac{3}{2}$

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Most popular questions from this chapter

The limit of the product of two functions equals the ____ of their limits.

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

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

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

Find $\lim_{x \to 2^{-}} f (x)$ .

In Problems 45-60, determine whether $f$ is continuous at $c$ .

$f (x) = x^{3} - 3 x^{2} + 2 x - 6, c = 2$

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

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

See all solutions

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