   Chapter 10.3, Problem 51E 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 → 9 x − 3 x − 9

To determine

To calculate: The value of limx9x3x9 algebraically and give reason, if limit does not exist.

Explanation

Given Information:

The provided limit is limx9x3x9.

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,

limx9x3x9

Now, x3x9 is a closed-form function, but x=9 does not lies within its domain:

So, continuity of closed form theorem cannot be applied:

Try to simplify the expression:

limx9x3x9=limx9(x3)(x+3)(x9)(x+3)

Apply the sum and difference formula (ab)(a

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