   Chapter 2, Problem 4RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the limit. lim x → 3 x 2 − 9 x 2 + 2 x − 3

To determine

To find: The value of limx3x29x2+2x3.

Explanation

Definition 1: “A function f is continuous at a number a if limxaf(x)=f(a)”.

Theorem 1: “Any rational function is continuous wherever it is defined”.

Calculation:

Obtain the limit of the function by using the Definition 1.

Let f(x)=x29x2+2x3 be a rational function in which {x| x3}.

By Theorem 1, the rational function f(x) is continuous on the domain {x| x3}.

Moreover, from Definition 1, the limit can be expressed as limxaf(x)=f(a) for continuous function

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