Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 2.3, Problem 26E

To determine

To find: The formula for the extended function f(x)=x3−1x2−1 such that f(x) is continuous at x=1 .

Expert Solution & Answer

Answer to Problem 26E

The formula for the extended function f(x)=x3−1x2−1 such that f(x) is continuous at x=1 is y=x2+x+1x+1 .

Explanation of Solution

Given information:

The function is f(x)=x3−1x2−1 and the point is x=1 .

Calculation:

The value of the function f(x)=x3−1x2−1 at x=1 doesn’t exist.

Simplify the given function.

f(x)=x3−1x2−1=(x−1)(x2+x+1)(x−1)(x+1)=x2+x+1x+1

The function y=x2+x+1x+1 is a quotient of two polynomial functions and it is continuous at x=1 .

Therefore, the formula for the extended function f(x)=x3−1x2−1 such that f(x) is continuous at x=1 is y=x2+x+1x+1 .

Chapter 2.3, Problem 25E

Chapter 2.3, Problem 27E

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

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The formula for the extended function f ( x ) = x 3 − 1 x 2 − 1 such that f ( x ) is continuous at x = 1 .