Chapter 2.5, Problem 4CQ

### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

Chapter
Section

### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
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

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