   Chapter 10.3, Problem 36E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 21-74, calculate the limit algebraically. If the limit does not exit, say why, lim x → − 1 x 2 + 3 x + 2 x 2 + x

To determine

To calculate: The value of limx1x2+3x+2x2+x algebraically and give reason, if limit does not exist.

Explanation

Given Information:

The provided limit is limx1x2+3x+2x2+x.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

Calculation:

Consider the limit,

limx1x2+3x+2x2+x

Now, x2+3x+2x2+x is a closed-form function, but x=1 does not lie within its domain. So, continuity of closed form theorem cannot be applied.

Try to simplify the limit by factored the equation:

limx1x2+3x+2x2+x=limx1x2+2x+x+2

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