   Chapter 10.3, Problem 52E 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 → 4 x − 4 x − 2

To determine

To calculate: The value of limx4x4x2 algebraically and give reason, if limit does not exist.

Explanation

Given Information:

The provided limit is limx4x4x2.

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)

The sum and difference formula is used:

(ab)(a+b)=a2b2

Calculation:

Consider the limit limx4x4x2.

Now, x4x2 is a closed-form function, but x=4 does not lies within its domain: So, continuity of closed form theorem cannot be applied:

Try to simplify the expression:

limx4x4x2=limx4(x4)(x+2)(x2)(x+2)

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