BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 2, Problem 4RE
To determine

To find: The value of limx3x29x2+2x3.

Expert Solution

Answer to Problem 4RE

The limit of the function is 0.

Explanation of Solution

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.

limxaf(x)=limx3x29x2+2x3=(3)29(3)2+2(3)3=999+63=0

Thus, the limit of the function is 0.

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