   Chapter 9, Problem 28RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 25-30, suppose that f ( x ) = { x 2 + 1         if  x ≤ 0 x                if  0 < x < 1 2 x 2 − 1       if  x ≥ 1 Is f ( x ) continuous at x = 0 ?

To determine

Whether the function, f(x)={x2+1      if x0x           if 0<x<12x21   if x1 is continuous at x=0.

Explanation

Given Information:

The function is, f(x)={x2+1      if x0x           if 0<x<12x21   if x1.

Explanation:

Consider the provided function,

f(x)={x2+1      if x0x           if 0<x<12x21   if x1

A function f(x) is continuous at x=c if the limit limxcf(x) exists. So, to check whether the function is continuous at x=0, consider the limit,

limx0f(x)

The limxcf(x) will exist at c if,

limxcf(x)=limxc+f(x)

Now, the limit from the left is represented by limx0f(x) and the limit from the right is represented by limx0+f(x).

The limxcf(x) will exist at c=0 when the limit from the left, that is, the values of f(c) but c<0, is equal to the limit from the right, that is, the values of f(c) but c>0

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