   Chapter 9.1, Problem 29E 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 15-40, use properties of limits and algebraic methods to find the limits, if they exist. lim x → − 2 x 2 + 4 x + 4 x 2 + 3 x + 2

To determine

To calculate: The value of the limit limx2x2+4x+4x2+3x+2.

Explanation

Given Information:

The limit is limx2x2+4x+4x2+3x+2.

Formula used:

If limxaf(x)=0 and limxag(x)=0, then limxaf(x)g(x) has indeterminate form (00), and factor xa from f(x)andg(x), reduce the fraction and then find the limit of the final expression.

A limit limxax can be simplified as,

limxax=a

Calculation:

Consider the provided limit,

limx2x2+4x+4x2+3x+2

Simplify the limit by substituting 2 for x,

limx2x2+4x+4x2+3x+2=(2)2+4(2)+4(2)2+3(2)+2=48+446+2=00

Since, the limit has 00 indeterminate form at x=2

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