   Chapter 2.5, Problem 21E

Chapter
Section
Textbook Problem

Explain why the function is discontinuous at the given number a. Sketch the graph of the function. f ( x ) = { cos x   if   x < 0 0       if   x = 0 1 − x 2     if   x > 0 a = 0

To determine

To explain: The function f(x)={cosxif x<10if x=01x2if x>0 is discontinuous at the number a=0 and sketch the graph of the function f(x)={cosxif x<10if x=01x2if x>0.

Explanation

Definition used: “A function f is continuous at a number a if limxaf(x)=f(a)”.

Note 1: “If f is defined near a, f is discontinuous at a whenever f is not continuous at a”.

Theorem: The limit limxaf(x)=L if and only if limxaf(x)=L=limxa+f(x).

Calculation:

By note 1, the function f is said to be discontinuous at x=a if anyone of the following conditions does not satisfied.

• f(a) is defined
• The limit of the function at the number a exists.
• limxaf(x)=f(a)

Consider the piecewise function f(x)={cosxif x<10if x=01x2if x>0.

Here, the function f(x) is defined at x=a. That is, f(0)=0 is defined.

The limit of the function f(x) as x approaches a=0 is computed as follows

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 126. 1x9x3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Let A={2,4,6,8} and B={6,7,8,9,10}. Compute: a. n(A) b. n(B) c. n(AB) d. n(AB)

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: Predator-prey population models are the solutions to two differential equations.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

For what values of p does the series converge?

Study Guide for Stewart's Multivariable Calculus, 8th

Explain the distinction between a hypothesis and a prediction.

Research Methods for the Behavioral Sciences (MindTap Course List) 