continuity

• Jun 1st 2010, 04:18 PM
wolfxpax
continuity
plz help,

at x=3 the function given by

f(x)= x^2 , x<3
6x-9 , x ≥ 3
is the function both continuous and differentiable?
• Jun 1st 2010, 04:35 PM
skeeter
Quote:

Originally Posted by wolfxpax
plz help,

at x=3 the function given by

f(x)= x^2 , x<3
6x-9 , x ≥ 3
is the function both continuous and differentiable?

what are the requirements for a function to be continuous at a value x = c ?
• Jun 1st 2010, 08:19 PM
wolfxpax
its needs to be defined?
• Jun 2nd 2010, 03:01 AM
HallsofIvy
Rule I: If you do not know the meaning of words in a problem, do not even start on the problem until you have looked up those words!

No, just being "defined" at a point does not mean a function is continuous or differentiable at that point. What is the definition of "continuous"? What is the definition of "differentiable"?
• Jun 2nd 2010, 04:40 AM
skeeter
Quote:

Originally Posted by wolfxpax
its needs to be defined?

have a look at the link ...

Pauls Online Notes : Calculus I - Continuity