Chapter 1: Q. 11 (page 119)

Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.
$\lim_{x \to 0^{-}} f (x) = - 1, \lim_{x \to 0^{+}} f (x) = 1, f (0) = 0 .$

Short Answer

Expert verified

The type of discontinuity is a jump discontinuity and there is not any one-sided continuity.

The possible graph of fis

Step by step solution

Step 1. Given Information.

The given function is $\lim_{x \to 0^{-}} f (x) = - 1, \lim_{x \to 0^{+}} f (x) = 1, f (0) = 0 .$

Step 2. Describing the discontinuity.

From the function, we can depict that $\lim_{x \to 0^{-}} f (x) = - 1 and \lim_{x \to 0^{+}} f (x) = 1$ both exist but are not equal to $f (0) = 0 .$

Thus,f(x)has a jump discontinuity at $x = 0 .$

Step 3. Describing one-sided continuity at x=c.

There is not any one-sided continuity at $x = 0$ because $\lim_{x \to 0^{-}} \neq f (0) and \lim_{x \to 0^{+}} \neq f (0) .$

Step 4. Graph of f.

The graph of fis

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Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.
$\lim_{x \to 0^{-}} f (x) = - 1, \lim_{x \to 0^{+}} f (x) = 1, f (0) = 0 .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Describing the discontinuity.

Step 3. Describing one-sided continuity at x=c.

Step 4. Graph of f.

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Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.limx→0-f(x)=-1,limx→0+f(x)=1,f(0)=0.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Describing the discontinuity.

Step 3. Describing one-sided continuity at x=c.

Step 4. Graph of f.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Geometry

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Calculus

Study anywhere. Anytime. Across all devices.

Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.
$\lim_{x \to 0^{-}} f (x) = - 1, \lim_{x \to 0^{+}} f (x) = 1, f (0) = 0 .$