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Fill in the blanks to complete the following proof. Claim: The function f(x) = x³ + 2 is continuous at a = 0. Proof: Given € > 0, choose d = VE. Then < 6 we have f(x) – ƒ(0)| - |x^2 |x^3+2| < 83 = €, as required. for all x^3 = |x| xER with . But there exists

Fill in the blanks to complete the following proof. Claim: The function f(x) = x³ + 2 is continuous at a = 0. Proof: Given € > 0, choose d = VE. Then < 6 we have f(x) – ƒ(0)| - |x^2 |x^3+2| < 83 = €, as required. for all x^3 = |x| xER with . But there exists

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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Fill in the blanks to complete the following proof. Claim: The function f(x) = x³ + 2 is continuous at a = 0. Proof: Given € > 0, choose d = VE. Then < 6 we have |ƒ(x) — ƒ(0)| = = <8³ |x|^2 |x^3+21 = €, as required. O for all x^3 |x| x ER with . But there exists
Transcribed Image Text:Fill in the blanks to complete the following proof. Claim: The function f(x) = x³ + 2 is continuous at a = 0. Proof: Given € > 0, choose d = VE. Then < 6 we have |ƒ(x) — ƒ(0)| = = <8³ |x|^2 |x^3+21 = €, as required. O for all x^3 |x| x ER with . But there exists
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