Chapter 14: Q. 27 (page 906)

Is $f$ continuous at $4$ ?

Short Answer

Expert verified

$f (x)$ is continuous at $x = 4$ .

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 x=4

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

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

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

Since $\lim_{x \to 4^{-}} f (x) = \lim_{x \to 4^{+}} f (x) = f (4)$ , $f (x)$ is continuous at $4$ .

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Is $f$ continuous at $4$ ?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine f(x) is continuous at x=4

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Is f continuous at 4?

Short Answer

Step by step solution

Step 1. Graph the function f(x)

Step 2. Determine f(x) is continuous at x=4

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Statistics

Decision Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Is $f$ continuous at $4$ ?