   Chapter 9.1, Problem 32E ### 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 → 2 f ( x ) , where  f ( x ) = { x 3 − 4 x − 3 if  x ≤ 2 3 − x 2 x  if  x > 2

To determine

To calculate: The value of limx2f(x) for the function f(x)={x34x3ifx13x2xifx>1.

Explanation

Given Information:

The limit is limx2f(x). The function is f(x)={x34x3ifx13x2xifx>1.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

Calculation:

Consider the provided limit,

limx2f(x)

The limit from the left is represented by limx2f(x) and the limit from the right is represented by limx2+f(x).

The limxcf(x) will exist at c=2 when the limit from the left, that is, the values of f(c) but c<2, is equal to the limit from the right, that is, the values of f(c) but c>2.

Consider the limit from the left,

limx2f(x)

Substitute x34x3 for f(x),

limx2f(x)=limx2(x3&#

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