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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.
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The crux of the matter is this: what is the "calculus definition" of continuity at a point?
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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.
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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?