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.
The function f is said to be of (differentiability) class Ck if the derivatives fâ², fâ²â², ..., f(k) exist and are continuous (the continuity is implied by differentiability for all the derivatives except for f(k)). The function f is said to be of class Câ, or smooth, if it has derivatives of all orders.