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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?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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?

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
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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