4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition) and do only d and e please ASAP 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.

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Answered: (d) f(x) = arctan x on R. (e) f(x) =…

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(d) f(x) = arctan x on R. (e) f(x) = 1/(1+ x²) on R.

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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Question

4. Determine whether or not the following functions are uniformly continuous.
(Use ε and δ to prove your work through e delta definition) and do only d and e please ASAP

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.

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