Home > Calculus > Definition of Continuity at a Point

What are the three conditions for continuity at a point?

Answer 1

Emilia Aguilar

A function #f(x)# is continuous at a point #(a,b)# if and only if:

#f(a)# is defined;
#lim_(xrarra) f(x)# is defined; and
#lim_(xrarra) f(x) =b#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Christopher Allers

The three conditions for continuity at a point are:

The function must be defined at that point.
The limit of the function as x approaches that point must exist.
The value of the function at that point must be equal to the limit of the function at that point.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.