# Limit/Derivative Problem

• August 29th 2010, 07:42 PM
RU2010
Limit/Derivative Problem
I'm having trouble getting started with a calculus problem, can anyone help me?

The limit $\lim_{x \to 4} \frac{\sqrt{x}-2}{x-4}$ 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...
• August 29th 2010, 09:06 PM
pickslides
Well as $x\to 4$ the point is $x=4$

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

What methods for taking limits have you been taught?
• August 30th 2010, 03:17 PM
RU2010
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?
• August 30th 2010, 03:23 PM
skeeter
$\displaystyle f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x-a}$
• August 30th 2010, 03:29 PM
RU2010
Makes perfect sense now! Thanks so much!