/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 32 In Problems 13鈥�32, use the acc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 32 (page 889)

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Is f continuous at 5?

Short Answer

Expert verified

The answer is Yes. The function is continuous at 5.

Step by step solution

01

Step. 1 How to check continuity? 

For a function to be continuous its LHL = RHL = f(c) at the point x=c.

02

Step. 2 Calculating LHL, RHL and f(c).

Firstly we calculate f(5)which is equal to 1 as given in the graph.

Now, we calculate LHL which is,

limx鈫�5-f(x)=1.

Finally we see RHL which is,

limx鈫�5+f(x)=1.

From here we can see thatLHL=RHL=f(5)limx鈫�5-f(x)=limx鈫�5+f(x)=f(5)=1

So, all the conditions to check continuity passes. That's why, the function is continuous at x=5.

And from the graph itself we can clearly see that we don't have to pick our pencil up the paper when we move through x=5which is also a method to check whether the function is continuous or not.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 7鈥� 42, find each limit algebraically.

limx鈫�23x-25/2.

limx鈫�cx=___

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
limx鈫�0f(x),f(x)=x-1ifx<03x-1ifx鈮�0

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Findlimx鈫�-6-f(x).

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�-3f(x),f(x)=2x
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.