2. Is the function f(x) = 1/x2 uniformly continuous on (0, 1)? Justify youranswer.

4. Using only the definition of uniform continuity, prove that the functionf(x) = x/(x + 1) is uniformly continuous on [0, ).

7. Prove that if I is a bounded interval and f is an unbounded function defined on I, then f cannot be uniformly continuous.

8. Let f be a function defined on an interval I and suppose that there arepositive constants K and r such that|f(x) f(y)| K|x y|^r for all x, y I.Prove that f is uniformly continuous

10. Is the function f(x) = x sin 1/x uniformly continuous on (0, 1)? Justifyyour answe