1. Construct a function on [0, 1] that is not Riemann Integrable. Prove that it is not integrable by showing that U(f) > L(f). 2. Give a bounded differentiable function on (0, 1) whose derivatives are unbounded. Demonstrate this for your function. 3. Give a function f which is non-continuous at c but where H(x) = f f is differentiable. 4. Give a function that is continuous and differentiable on [0, }) and (}, 1] for which the result of the mean value theorem is not true. 5. Give a sequence of functions fo that converge point-wise to 0 but where each fn has the property that Sa fn = 1. 6. Continuous functions on [a, b] attain their min and max values. Give an example of a function that is continuous on (a, b) but which does not attain it's inf or sup on [a, b] (ie. inf(f)