1. ## Analysis

Hey all,

I was wondering if there is a function such that
a) f(3) exists, lim x->3 f(x) exists, but f is not continuous at 3

Does such a function exist? or is it impossible?

2. Originally Posted by thahachaina
Hey all,

I was wondering if there is a function such that
a) f(3) exists, lim x->3 f(x) exists, but f is not continuous at 3

Does such a function exist? or is it impossible?
The following function satisfies your criteria:

$\displaystyle f(x) = | x- 3|$, $\displaystyle x \neq 0$, and at x = 3 f(x) = 1.

There are an infinite number of other functions that also satisfy the criteria.

3. Hey man, thanks for the help. But i didn't get how is f(x)=1 when x=3? Also, does x is not equal to zero a condition? Sorry if thats dumb, but could you please explain a little. Thanks once again

4. Originally Posted by thahachaina
Hey man, thanks for the help. But i didn't get how is f(x)=1 when x=3? Also, does x is not equal to zero a condition? Sorry if thats dumb, but could you please explain a little. Thanks once again
I have defined the following function:

I have defined f(x) = |x - 3| for all values of x except for x = 3. When x = 3 I have defined the function to equal 1.