The value of lim x → 3 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 4RE
To determine

To find: The value of limx→3x2−9x2+2x−3.

Expert Solution

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.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!