Problem 554 (difficulty: 4/10)

Are the following functions uniformly continuous?

a) \(\displaystyle x^2\) on \(\displaystyle (1,2)\),

b) \(\displaystyle \sin x\) on \(\displaystyle \R\),

c) \(\displaystyle \sin{1\over x}\) on\(\displaystyle (0,\infty)\),

d) \(\displaystyle 1/x\) on \(\displaystyle (0,2)\),

e) \(\displaystyle \sqrt{x}\) on \(\displaystyle (0,\infty)\).

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