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Assignment 1
a) Investigate if f(x) = x5 ln x is uniformly continuous on [1, 2].
b) Investigate if f(x) = πx^2 is uniformly continuous on (-∞, ∞).
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c) Investigate if f(x) = x2 cos(𝑥) is uniformly continuous on (0, 1].
d) Investigate if f(x) = ln(x4 + 1) is uniformly continuous on (-∞, ∞).
e) Give an example where f is not differentiable on [0, ∞), but is uniformly continuous.
f) Determine if the functions are uniformly continuous on their domain:
i) f : (0,∞) → R,
f(x) = x3 sin(
ii) g : (−∞,∞) → R+,
g(x) = e-x^2
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)
x^2
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