In the attached calculation, why does it say it is the quotient of the two polynomials? Does that mean in most of the cases with these problems we can just simplify the original function to get the extended function? Is an extended function just finding the limit of a function and filling in the removable discontinuity?
In the attached calculation, why does it say it is the quotient of the two polynomials? Does that mean in most of the cases with these problems we can just simplify the original function to get the extended function? Is an extended function just finding the limit of a function and filling in the removable discontinuity?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
Question
In the attached calculation, why does it say it is the quotient of the two polynomials? Does that mean in most of the cases with these problems we can just simplify the original function to get the extended function? Is an extended function just finding the limit of a function and filling in the removable discontinuity?

Transcribed Image Text:To determine
To find: The formula for the extended function f (x) = such that f (x) is continuous at x = 1.
Expert Solution & Answer
Answer to Problem 26E
The formula for the extended function f(x) = such that f (x) is continuous at x = 1 is y = x+1
x²+x+1
Explanation of Solution
Given information:
The function is f (x)
x²-1
(x-1)(x²+x+1)
(x-1)(x+1)
=
Calculation:
The value of the function f (x) =
Simplify the given function.
f (x) =
=
x²+x+1
x+1
The function y
x²+x+1
x+1
=
-
x²-1
and the point is x = 1.
x²+x+1
x+1
at x = 1 doesn't exist.
Therefore, the formula for the extended function f (x)
=
y =
SAVE
is a quotient of two polynomial functions and it is continuous at x = 1.
such that f (x) is continuous at x = 1 is
x²-1
Σ
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