Chapter 9.1, Problem 29E

### Mathematical Applications for the ...

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

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 limxâ†’âˆ’2x2+4x+4x2+3x+2.

Formula used:

If limxâ†’af(x)=0 and limxâ†’ag(x)=0, then limxâ†’af(x)g(x) has indeterminate form (00), and factor xâˆ’a from f(x)andg(x), reduce the fraction and then find the limit of the final expression.

A limit limxâ†’ax can be simplified as,

limxâ†’ax=a

Calculation:

Consider the provided limit,

limxâ†’âˆ’2x2+4x+4x2+3x+2

Simplify the limit by substituting âˆ’2 for x,

limxâ†’âˆ’2x2+4x+4x2+3x+2=(âˆ’2)2+4(âˆ’2)+4(âˆ’2)2+3(âˆ’2)+2=4âˆ’8+44âˆ’6+2=00

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

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