   Chapter 2.5, Problem 4CQ

Chapter
Section
Textbook Problem

Suppose lim x → a − f ( x ) = L and lim x → a + f ( x ) = M , where L and M are real numbers. What conditions on L, M, and f(a) will guarantee that f is continuous at x = a?

To determine
The condition at which the function is continuous at x=a .

Explanation

Given information:

The function limxa+f(x)=L and limxaf(x)=M , where L and M are real numbers.

Calculation:

The function f has the right hand limit L as x approaches a from the right that is limxa+f(x)=L .

The function f has the left hand limit M as x approaches a from the left that is limxaf(x)=M .

The function f(x) is continuous at x=a if L=M=f(a) which is shown below through the example.

f(x)={xifx0xif

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

Prove that limx0x2cos(1/x2)=0.

Calculus: Early Transcendentals

Find the value of k such that (k,k) is equidistant from (1,0) and (0,2).

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the limit. limx0sin(x2)x

Single Variable Calculus: Early Transcendentals, Volume I

In Problems 39 – 44, solve each inequality and graph the solution. 39.

Mathematical Applications for the Management, Life, and Social Sciences

Change each percent to a decimal: 27%

Elementary Technical Mathematics 