Hi,

So I'm trying to fully understand the theorem that suggests if "f" is differentiable at "a", then "f" is continuous at "a".

The issue that i'm facing with this definition is when I'm dealing with function which have holes in them, such asf(x) = (x^2-4)/(x-2)which then simplify's tof(x) = x+2, such that x does not equal 2.

So even though f(x) is differentiable, the function is not continuous given that it has a hole at x = 2. Can someone please let me know whether or not my logic is right about this? This is the only idea that is getting in the way of me understanding the relationship between differentiability and continuity. Really what I'm doing here is disproving the theorem that I stated above (I believe), and I would really appreciate someone to explain why or why not I may be wrong.

Please help!

Olivia