A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either undefined or...

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.

The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:

The intestinal epithelial lining rapidly renews every 4 to 5 days. The renewal is facilitated by intestinal stem cells (ISCs) located at the base of the crypt– a gland located at the bottom of each villus. ISCs divide asymmetrically to form new stem cells and progenitor daughter cells. The daughter cells are called transit-amplifying (TA) cells which move upwards along the crypt and either differentiate into absorptive cells– the enterocytes or secretory cells– including the goblet,...

The skin is divided into epidermis, dermis, and hypodermis, the skin's outermost, middle, and inner layers. The human epidermal layer regularly undergoes renewal, where old, dead cells are replaced by new cells. Epidermal stem cells or EpiSCs divide and differentiate to restore the lost cells. For the renewal process, some EpiSCs continuously self-renew. In contrast, few others differentiate into transit-amplifying cells, which later form prickle or spinous cells, followed by granular cells,...

Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period of time is called the flow rate Q, or more precisely, the volume flow rate. Flow rate and velocity are related—for instance, a river has a greater flow rate if the velocity of the water in it is greater. However, the flow rate also depends on the size and shape of the river. The relationship between flow rate (Q) and average speed (v)...