Right and left continuous limits

Question

Suppose f(x) =2 f x<3 and f(x) = —4 for x>3.

a) what is f(3) if f is left continious at x=3
b) what is f(3) if f is right continuos at x=3

 

I really have no idea how to do this. 

Answer 1

Here are the necessary ideas for you to grasp:

 

a) The left limit of f at 2, which involves 'imagining' x coming toward 3 FROM THE LEFT, is the value 2

 

b) The right limit of f at 2, coming toward 2 FROM THE RIGHT, is -4

 

Since at 3 the left & right limits do not agree, there is no limit at 3 (because there are two different contending answers).

 

This function is CONTINUOUS (note spelling) except at 3, which is not in its domain.