The crux of the matter is this: what is the "calculus definition" of continuity at a point?
Hey, need help with some calculus stuff.
if f(x) = (sqrt(2x+5)-sqrt(x+7)) / (x-2) for x ≠ 2, and if f is continuous at x = 2, then k = ?
f(2) = k
Sorry, I don't know how to do the symbols, so I had to type it out like this. sqrt = square root.
I also need to know how you do it, not just the answer.
Thanks in advance for the help. I really appreciate it.
The calculus definition of continuity at a point (which is entirely equivalent to the epsilon-delta definition) goes like this: function is continuous at if and only if
This statement means three things:
1. The limit exists.
2. The function is defined at that is, exists.
3. The limit is equal to the function's value at
Any one of those could fail, leaving you with a discontinuous function at
So, does this give you any ideas?