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11. Define f: R→ R by f(x) = 8x if x is rational and f(x) = 2x² + 8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1.

11. Define f: R→ R by f(x) = 8x if x is rational and f(x) = 2x² + 8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1.

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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I need to prove using definition of continuity that f is continuous at 2 and discontinuous at 1. If you can't do it then please leave it for someone who can. I don't want to do it the other way, Thanks

11 Define f: RR by f(x) = 8x if x is rational and f(x) = 2x² + 8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1. 3.2 ALGEBRA OF CONTINUOUS FUNCTIONS *12. Let p and q be polynomials and xo be a zero of q of multiplicity m. Prove that p/q can be assigned a value at xo such that the function thus defined will be continuous there iff xo is a
Transcribed Image Text:11 Define f: RR by f(x) = 8x if x is rational and f(x) = 2x² + 8 if x is irrational. Prove from the definition of continuity that f is continuous at 2 and discontinuous at 1. 3.2 ALGEBRA OF CONTINUOUS FUNCTIONS *12. Let p and q be polynomials and xo be a zero of q of multiplicity m. Prove that p/q can be assigned a value at xo such that the function thus defined will be continuous there iff xo is a
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