   Chapter 9.1, Problem 31E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 15-40, use properties of limits and algebraic methods to find the limits, if they exist. lim x → − 1 f ( x ) , where  f ( x ) = { x 2 + 4 x  if  x ≤ − 1 3 x 3 - x -1 if  x > − 1

To determine

To calculate: The value of limx1f(x) for the function f(x)={x2+4xifx13x3x1ifx>1.

Explanation

Given Information:

The limit is limx1f(x). The function is f(x)={x2+4xifx13x3x1ifx>1.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

Calculation:

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.

Consider the limit from the left,

limx1f(x)

Substitute x2+4x for f(x),

limx1f(x)=limx1(x2+4

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