1. ## Limit/Derivative Problem

I'm having trouble getting started with a calculus problem, can anyone help me?

The limit $\displaystyle \lim_{x \to 4} \frac{\sqrt{x}-2}{x-4}$ represents the derivative of a function taken at a point. What function? What point? What is the limit?

I need help getting started with this problem...

2. Well as $\displaystyle x\to 4$ the point is $\displaystyle x=4$

I get $\displaystyle \displaystyle \lim_{x \to 4} \frac{\sqrt{x}-2}{x-4}= \frac{1}{4}$

What methods for taking limits have you been taught?

3. Sorry, I didn't really explain this problem well. I knew the answer to the acutal limit, and the point, but I'm having trouble figuring out what function this represents the derivative taken at a point of.

If this limit represents the numerical derivative of 1/4 taken at x=4, what would the original function that I'm taking the derivative of be?

Thanks?

4. $\displaystyle \displaystyle f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}$

5. Makes perfect sense now! Thanks so much!