# The value of lim x → 1 + x 2 − 9 x 2 + 2 x − 3 .

### 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 6RE
To determine

## The value of limx→1+x2−9x2+2x−3.

Expert Solution

The value of limx1+x29x2+2x3=.

### Explanation of Solution

Express the given function as follows.

limx1+x29x2+2x3=limx1+x29x2+2x3=limx1+(x+3)(x3)(x+3)(x1)=limx1+(x3)(x1)

Since x is closer to 1 from right side (that is, x>1), the denominator (x1) is a small positive number (=0) and the numerator (x3) is a negative number.

Hence, the quotient is a numerically larger negative number.

Therefore, it can be concluded that, limx1+x29x2+2x3=.

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