The function is continuous at 0. The calculus definition of continuity is as followed: A function is continuous at a point if both the and the exist and the .
Hace a problem that asks me to determine if the following function;
f(x) = if x<0
and , if
is continuous at x = 0 and then if it's differentiable at x=0,
I figured to compute the limit as x -> 0 from x<0 and x>0 to determine continuity.
when i did lim(x->0) i used lhopitals to give 1/1 which isnt equal to f(0) = 0 so i figured the function wasn't continuous.
But i assume i have made a mistake here as when i went ahead and checked for differentiability i found the function to be diff at x=0. which doesn't make sense as if differentiable it must be continuous?
Please help.
Cheers.
Yes, that is correct.
No,which isnt equal to f(0) = 0
so i figured the function wasn't continuous.
But i assume i have made a mistake here as when i went ahead and checked for differentiability i found the function to be diff at x=0. which doesn't make sense as if differentiable it must be continuous?
Please help.
Cheers.