# The value of lim r → 9 r ( r − 9 ) 4 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2, Problem 9RE
To determine

Expert Solution

## Answer to Problem 9RE

The value of limr9r(r9)4=.

### Explanation of Solution

Consider the left hand limit limr9r(r9)4.

Since r approaches 9 (but smaller than 9), the denominator (r9)4 becomes a small positive number (= 0) and the numerator r becomes a positive number which is almost close to 3. Hence, the quotient is a larger positive number.

Therefore, it is obvious that, limr9r(r9)4=.

Consider the right hand limit limr9+r(r9)4.

Since x approaches 9 (but greater than 9), the denominator (r9)4 becomes a small positive number (= 0) and the numerator r is very close to 3. Hence, the quotient is a larger positive number.

Therefore, it is clear that, limr9+r(r9)4=.

Since the left hand and the right hand limits are equal, it can be concluded that limr9r(r9)4=.

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