1 The water-soluble vitamins (B vitamins and vitamin C) are absorbed easily along with the water in the small intestine, where they then travel through the body via the blood vessels. 2  Fat-soluble vitamins (vitamins A, D, and K) are absorbed just like the fat mentioned above.
A function f is said to be continuously differentiable if the derivative f'(x) exists and is itself a continuous function. Though the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity. For example, the function.
PROBLEM 8 : Use the limit definition to compute the derivative, f'(x), for . Click HERE to see a detailed solution to problem 8. PROBLEM 9 : Assume that Show that f is differentiable at x=1, i.e., use the limit definition of the derivative to compute f'(1) . Click HERE to see a detailed solution to problem 9.