4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition) 4. Determine whether or not the following functions are uniformly continuous.(a) f(x) = Vx on (0, 0).(b) f(x) = x sin(1/x) for x 0 and f(0) = 0 on [–T, 7].(c) f(x) = x- sin x if x +0 and f(0) = 1 on R.(d) f(x) = arctan x on R.(e) f(x) = 1/(1+ x²) on R.

Given the function (a) fx=x on 0,∞ By the mean value theorem Let f=xα and x<y Since,…

Answered: 4. Determine whether or not the…

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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4. Determine whether or not the following functions are uniformly continuous. (a) f(x) = Vx on (0, ∞0). (b) f(x) = x sin(1/x) for x # 0 and f(0) = 0 on [–T, 7|]. (c) f(x) = x¯' sin x if x + 0 and f(0) = 1 on R. (d) f(x) (e) f(x) = 1/(1 + x²) on R. = arctan x on R.