Chapter 14: Q. 11 (page 907)

In Problems 8–12, use the accompanying graph of $y = f (x)$
Does $\lim_{x \to 1} f (x)$ exist? If so, what is it? If not, explain why not?

Short Answer

Expert verified

The limit exists that is $\lim_{x \to 1} f (x) = 2$

Step by step solution

Step 1. General formula

The value of a limit is found by using,

$\lim_{x \to c^{-}} f (x) = \lim_{x \to c^{+}} f (x) = \lim_{x \to c} f (x)$

It is clear from the graph,

$\lim_{x \to 1^{-}} f (x) = 2 \lim_{x \to 1^{+}} f (x) = 2$

Step 2. Value of the limit

We have found that,

$\lim_{x \to 1^{-}} f (x) = 2 = \lim_{x \to 1^{+}} f (x)$

Therefore,

$\lim_{x \to 1} f (x) = 2$

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In Problems 8–12, use the accompanying graph of $y = f (x)$
Does $\lim_{x \to 1} f (x)$ exist? If so, what is it? If not, explain why not?

Short Answer

Step by step solution

Step 1. General formula

Step 2. Value of the limit

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In Problems 8–12, use the accompanying graph ofy=f(x)Does limx→1f(x)exist? If so, what is it? If not, explain why not?

Short Answer

Step by step solution

Step 1. General formula

Step 2. Value of the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Pure Maths

Statistics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 8–12, use the accompanying graph of $y = f (x)$
Does $\lim_{x \to 1} f (x)$ exist? If so, what is it? If not, explain why not?