f:R-->R
f(x)=1 if
f(x)=0 otherwise.
(a) Is f continuous at the point a = 0?
(b) Is f continuous at the point a = 1?
have i done them correctly?
Continuous at a=0 because correct?
also continuous at a=1 because
thanks
Are you really sure of the first case? When you are not at 0 (which you aren't when you are taking a limit), the function takes the value 0. What does converge to?
I mean you can think about it more intuitively, is the function "connected" at 0? Draw it.
I see what you mean. The function is not connected at zero and hence the limit in first case doesn't exist so not continuous at a=0
The limit does exist! Try to compute it this way
what it the limit of this sequence? (it's the same as ).
I think it may help if you look up the definition of a limit. The limit at a=0 might not be f(a) (which is the case here), but indeed it still does exist.