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Analysis proof excercise: The function f: R → R is defined by f(x) = 0 x is irrational x is rational x² Now use the definition of derivatives, prove that f is not differentiable at R⁄o, i.e., all real points except 0 DO NOT USE DISCONTINUOUS TO PROVE PLEASE! Use limx→a f(x)-f(a) x-a

Analysis proof excercise: The function f: R → R is defined by f(x) = 0 x is irrational x is rational x² Now use the definition of derivatives, prove that f is not differentiable at R⁄o, i.e., all real points except 0 DO NOT USE DISCONTINUOUS TO PROVE PLEASE! Use limx→a f(x)-f(a) x-a

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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Analysis proof excercise: The function ƒ : R → R is defined by f(x)= = 0 ₂2 x is irrational x is rational Now use the definition of derivatives, prove that f is not differentiable at R40, i.e., all real points except 0. DO NOT USE DISCONTINUOUS TO PROVE PLEASE! Use limx→a f(x)-f(a) x-a
Transcribed Image Text:Analysis proof excercise: The function ƒ : R → R is defined by f(x)= = 0 ₂2 x is irrational x is rational Now use the definition of derivatives, prove that f is not differentiable at R40, i.e., all real points except 0. DO NOT USE DISCONTINUOUS TO PROVE PLEASE! Use limx→a f(x)-f(a) x-a
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