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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 crux of the matter is this: what is the "calculus definition" of continuity at a point?
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.
The calculus definition of continuity at a point (which is entirely equivalent to the epsilon-delta definition) goes like this: function $\displaystyle f(x)$ is continuous at $\displaystyle a$ if and only if
$\displaystyle \displaystyle\lim_{x\to a}f(x)=f(a).$
This statement means three things:
1. The limit $\displaystyle \displaystyle\lim_{x\to a}f(x)$ exists.
2. The function $\displaystyle f(x)$ is defined at $\displaystyle a;$ that is, $\displaystyle f(a)$ exists.
3. The limit is equal to the function's value at $\displaystyle a.$
Any one of those could fail, leaving you with a discontinuous function at $\displaystyle a.$
So, does this give you any ideas?
