Continuity of a Function
Continuity of a Function: Overview
This topic covers concepts such as Continuity of a Function, Continuity of a Function at a Point, Discontinuity of a Function, Removable and Non-Removable Discontinuities, Ways to Remove a Removable Discontinuity, Infinite Discontinuity, etc.
Important Questions on Continuity of a Function
Find the value of and for which the function
is continuous for all in ,

Let be a polynomial of degree one and be a continuous and differentiable function defined by . If , then


Choose the correct statement on the continuity of the function given by at

Choose the correct comment explaining the continuity of the function f defined by

If is continuous at then

An example of a function which is continuous but not differentiable is

Consider the function . The value of so that is continuous at is -

Function has oscillatory discontinuity at point .

Function has oscillatory discontinuity at point .

Define the oscillatory discontinuity with one example.

This is the graph of a function .
Find the -value at which has an isolated point discontinuity.

This is the graph of a function . Dashed lines represent asymptotes.
Select the -value at which has an isolated point discontinuity.

This is the graph of a function . Dashed lines represent asymptotes.
Select the -value at which has a missing point discontinuity.

Let be defined as
The value of for which is continuous at is

If in the interval is continuous, then is equal to

Let and , where denotes signum function of . If is continuous for all value of , then the value of and respectively is

Number of points of which is discontinuous, where are . Find , where denotes .

Let , then the numbers of points where is discontinuous is

The number of points of discontinuity of the function in the interval are
