Question

If f’(5) = 3, find the
(f(x)-f(5))/(√x-√5)
limx->5

Answer 1

\[\LARGE \lim_{x\to5}\frac{f(x)-f(5)}{\sqrt x-\sqrt5}\] I'll just rewrite it better, if this is what you meant... (I don't know to solve it ! ...) hope someone else helps you out. Good Luck !

Answer 2

multipyly top and bottom by \(\sqrt{x}+\sqrt{5}\)

Answer 3

thanks kreshnik again, I am too technically uncapable to use some latex editor.

Answer 4

\[ \lim_{x\to5}\frac{f(x)-f(5)}{\sqrt x-\sqrt5}\frac{\sqrt x+\sqrt 5}{\sqrt x+\sqrt 5}\]
\[ \lim_{x\to5}\frac{f(x)-f(5)(\sqrt{x}+\sqrt{5})}{x-5}\]
\[f'(5)(\sqrt{5}+\sqrt{5})\]

Answer 5

last line since
\[ \lim_{x\to5}\frac{f(x)-f(5)}{ x-5}=f'(5)\] by definition

Answer 6

@satellite73 I didn't know that, I learned something new. Great job .