   Chapter 9.2, Problem 16E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 9-16, determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing each function with a graphing utility. f ( x ) = { x 3 + 10 if  x ≤ − 2 2 if  x > − 2

To determine

Whether the function, f(x)={x3+10   if x22           if x>2, is continuous or not, if the function is not continuous then find the point where it is discontinuous and to verify the conclusion by graphing the function by use of graphing calculator.

Explanation

Given Information:

The provided function is f(x)={x3+10   if x22           if x>2.

Explanation:

Consider the provided function,

f(x)={x3+10   if x22           if x>2

There are two different values of the function, f(x)=x3+10 for all x2 and f(x)=2 for all x>2.

Since, the function is equal to 2 for all values of x except x2, thus, the function is continuous for all values of x except x2.

A function, f, is continuous at x=c if f(c) exists, limxcf(x) exists and limxcf(x)=f(c).

The function is continuous at x=2 if the condition is satisfied

And the condition for continuous function:

limxcf(x)=limxc+f(x)=f(c)

To check whether the value of f(2) exists, substitute 2 for x in the function,

f(2)=(2)3+10=8+10=2

Thus, the value of f(2) is defined.

To check whether the limit, limx2f(x), exists, find the values of the left-limit and the right-limit. If the values of the left-limit and right-limit are equal, then the limit exists.

The limit from the left is represented by limx2f(x), that is, the values of f(2) but c<2

### 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

#### Evaluate the definite integral. 0T/2sin(2t/T)dt

Single Variable Calculus: Early Transcendentals, Volume I

#### Given that the point P(3, 5) lies on the line kx + 3y + 9 = 0, find k.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Exercises 516, evaluate the given quantity. log42

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate limn(1nn+1+1nn+2++1nn+n).

Single Variable Calculus: Early Transcendentals 