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Prove that the function f(x) = x³ is continuous at 2 directly using the definition (p. 83).

Prove that the function f(x) = x³ is continuous at 2 directly using the definition (p. 83).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the proof using the definition on page 83
DEFINITION Suppose ECR and f: E→ R. If xo E E, then f is continuous at xo iff for each e > 0, there is a 8 >0 such that if xxo < 8, XE E, then |f(x) = f(xo)| < €. If f is continuous at x for every x E E, then we say f is continuous.
Transcribed Image Text:DEFINITION Suppose ECR and f: E→ R. If xo E E, then f is continuous at xo iff for each e > 0, there is a 8 >0 such that if xxo < 8, XE E, then |f(x) = f(xo)| < €. If f is continuous at x for every x E E, then we say f is continuous.
nition (p. 34). 2. Prove that the function f(x) = x³ is continuous at 2 directly using the definition (p. 83).
Transcribed Image Text:nition (p. 34). 2. Prove that the function f(x) = x³ is continuous at 2 directly using the definition (p. 83).
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