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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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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