Chapter 14: Q. 26 (page 906)

Is $f$ continuous at $0$ ?

Short Answer

Expert verified

$f (x)$ is not continuous at $x = 0$ .

Step by step solution

Step 1. Graph the function f(x)

Let us graph $f (x)$ with the help of a graphing utility.

Step 2. Determine f(x) is continuous at 0

For a function to be continuous at $x = c$ , then the function must be defined at $x = c$ and $\lim_{x \to c^{-}} f (x) = \lim_{x \to c^{+}} f (x) = f (c)$ .

Let us consider the behavior of $f (x)$ near $x = 0$ .

When we consider the limit coming from the left side, the function approaches a value of $4$ .

That is $\lim_{x \to 0^{-}} f (x) = 4$

When we consider the limit coming from the right side, the function approaches a value of $1$ .

That is $\lim_{x \to 0^{+}} f (x) = 1$

Since $\lim_{x \to 0^{-}} f (x) \neq \lim_{x \to 0^{+}} f (x)$ , $f (x)$ is not continuous at $x = 0$ .

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Is $f$ continuous at $0$ ?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine f(x) is continuous at 0

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Is f continuous at 0?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine f(x) is continuous at 0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

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Mechanics Maths

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Decision Maths

Study anywhere. Anytime. Across all devices.

Is $f$ continuous at $0$ ?