   Chapter 9, Problem 27RE 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 What is lim x → 1 f ( x ) , if it exists?

To determine

To calculate: The value of limx1f(x) for the function, f(x)={x2+1      if x0x           if 0<x<12x21   if x1.

Explanation

Given Information:

The limit is limx1f(x). The function is f(x)={x2+1      if x0x           if 0<x<12x21   if x1.

Formula used:

The limxcf(x) will exist at c if,

limxcf(x)=limxc+f(x)

By the properties of limit limxcx can be simplified as, limxcx=c.

Calculation:

Consider the provided function,

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

Consider the provided limit,

limx1f(x)

The limit from the left is represented by limx1f(x) and the limit from the right is represented by limx1+f(x).

The limxcf(x) will exist at c=1 when the limit from the left, that is, the values of f(c) but c<1, is equal to the limit from the right, that is, the values of f(c) but c>1

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