Give an example of each of the following, or provide an argument for why the request is impossible. Assume that all of the functions discussed below are defined on all of R. (i) A function that is not continuous at a point but is differentiable at that point. (ii) Two distinct functions that are not differentiable at the same point but their product is differentiable at that point. (iii) Two functions, one of which is differentiable at some point a and the other is not differen- tiable at a, but their product is differentiable at the point a. (iv) Two functions, one of which is differentiable at some point a and the other is not differen- tiable at a, but their sum is differentiable at the point a. (v) A function that is differentiable at, and only at, one point.