# Ap Calc question.

• Nov 17th 2010, 09:16 AM
MasonJar
Ap Calc question.
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.
• Nov 17th 2010, 09:28 AM
Ackbeet
The crux of the matter is this: what is the "calculus definition" of continuity at a point?
• Nov 17th 2010, 09:55 AM
MasonJar
Um, I don't know. You're going to have to walk me through this one. I'm an idiot when it comes to Calculus. Every other math is easy for me. But Calculus is just something else.
• Nov 17th 2010, 10:43 AM
Ackbeet
The calculus definition of continuity at a point (which is entirely equivalent to the epsilon-delta definition) goes like this: function $f(x)$ is continuous at $a$ if and only if

$\displaystyle\lim_{x\to a}f(x)=f(a).$

This statement means three things:

1. The limit $\displaystyle\lim_{x\to a}f(x)$ exists.
2. The function $f(x)$ is defined at $a;$ that is, $f(a)$ exists.
3. The limit is equal to the function's value at $a.$

Any one of those could fail, leaving you with a discontinuous function at $a.$

So, does this give you any ideas?