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.
Analytic Function. A complex function is said to be analytic on a region if it is complex differentiable at every point in. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with analytic function (Krantz 1999, p. 16). complex function may fail to be analytic at one or more points through the presence of singularities, or along lines or line segments through the presence of branch cuts. A complex function that is analytic at all finite points of the complex plane is said to be entire.