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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F557ddcc0-78a8-42ad-8f72-70db02600943%2Fe25e6990-2eac-4a67-a41c-944412714983%2Ffey0pks_processed.jpeg&w=3840&q=75)
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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