# Limit and Continuity

## Short Questions

Define Continuity.

If the value of function and limit value of the function at the point 'a' are equal then the function is continuous at 'a'.

Define Discontinuity.

If the value of function and limit value of the function at the point 'a' are not equal then the function is discontinuous at 'a'.

Define Discontinuity.

An interval not containing both the end points 'a' and 'b' is known as open interval. It is denoted by (a, b).

Define Closed interval.

An interval containing both the end points 'a' and 'b' is known as closed interval. It is denoted by [a,b].

Define left hand limit.

The limit of f(x) is called left hand limit if x approaches to the point a from left. It is written as: $\lim \limits_{x \to a^-}$f(x)

Define right hand limit.

The limit of f(x) is called right hand limit if x approaches to the point a from right. It is written as: $\lim \limits_{x \to a^+}$f(x)

Define functional value.

The function y = f(x) assigns exactly one output (y = b) to each input (x = a) of a specified type. This output 'b' is called the value of the function at x = a.