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Chapter 14: Q. 23 (page 906)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Graph the function f(x)

We have been given $\lim_{x \to 2^{-}} f (x)$ .

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, let us consider the behavior of $f (x)$ near $x = 2$ when approaching from the left side.

The graph approaches $- \infty$ as $x$ approaches $2$ .

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

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Most popular questions from this chapter

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

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

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

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

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

$\lim_{x \to c} x =___$

Use the graph shown to determine if the limit exists. If it does, find its value.

See all solutions

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