LIMIT and CONTINUITY

In the 17th century several mathematicians developed the concepts of limits and continuity, primarily to foster the development of calculus. If f(x) gets closer and closer to q, as x gets close to p, then the limit of f, at p, is q. If f(p) = q then f is continuous at q. Intuitively, a continuous function can be graphed without lifting your pencil offf the paper, no gaps or jumps. Since this topic deals with limits and continuity in real space, it is sometimes called "real analysis".

LIMIT

In the mathematics, the major concept of limit is used to express a value that a sequence or function approaches as the input or key approaches of some value.

The concept of the Limit of function is further generalized to the concept of topological net, while the limit of a sequence is closely related to limit and direct limit in category theory.

In formulas, limit is usually abbreviated as lim as in lim(an) = a or represented by the right arrow (→) as in an → a.

Below is the one solved example on Limit.


CONTINUITY

Continuity means the function should not have any break or sudden jump at any point in the given domain. We have seen that any polynomial function P(x) satisfies:

for all real numbers a. This property is known as continuity.