Limits and Continuity

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In limits and continuity, the concept of limits leads to define and describe continuity and derivative of the function. The continuity of a function has practical as well as theoretical importance.

There are two types of limits:

Left hand limit and Right hand limit

Left Hand Limit: Let f(x) tend to a limit l₁ as x tends to a through values less than 'a', then l₁ is called the left hand limit.
Right Hand Limit: Let f(x) tend to a limit l₂ as x tends to 'a' through values greater than 'a', then l₂ is called the right hand limit.


A function f(x) is continuous on an interval I if and only if for each point a in I, the Math functions f(x) is continuous at x = a. (Here is understood that one sided limits are to be used at included endpoints of the interval I.)
Limit Order definition: Limit Order is an order placed with a brokerage to buy or sell a set number of shares at a specified price or better. Limit orders also allow an investor to limit the length of time an order can be outstanding before being canceled. Depending on the direction of the position, limit orders are sometimes referred to more specifically as a buy limit order, or a sell limit order.