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anonymous
 5 years ago
using the definition of a derivative find f(x)
=2/sqrt{x}
anonymous
 5 years ago
using the definition of a derivative find f(x) =2/sqrt{x}

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)= 2/ \sqrt{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this will be a pain to write out but not hard to compute. you must use the definition yes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i know that part i am having problems with rationalizing the denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you need to compute \[lim_{h>0}\frac{\frac{2}{\sqrt{x+h}}+\frac{2}{\sqrt{x}}}{h}\]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0Good opportunity to practice your LaTeX satellite! :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am learning. eventually i will be fluent in it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i know that part the step after that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok lets give me a break and at least factor out the 2, since this has nothing to do with the limit ok?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just factor out by 2 thats all you had t say lol thanks so much

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i knew that i was just doubting myself

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i knew that i was just doubting myself

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we will just write \[lim_{h>0}\frac{1}{\sqrt{x+h}}\frac{1}{\sqrt{x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0all divided by h of course. we worry about that last.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now we rationalize

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{\sqrt{x+h}}\frac{1}{\sqrt{x}}=\frac{\sqrt{x}\sqrt{x+h}}{\sqrt{x}\sqrt{x+h}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes multiply numerator and denominator by the conjugate of th enumerator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which of course is \[\sqrt{x}+\sqrt{x+h}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when you do that the numerator will just be \[xx+h=h\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and the denominator will be the product \[\sqrt{x} \sqrt{x+h}) (\sqrt{x}+\sqrt{x+h})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry am not repsonding i was working it out thanks i got it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats ok i was typing. did you get the numerator correctly? it is just h

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the denominator is that ugly thing i wrote last. so you have in total \[\frac{h}{h(\sqrt{x}\sqrt{x+h})(\sqrt{x}+\sqrt{x+h}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes they 'cancel' meaning they add to zero. and of course dividing by h means the h goes in the denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so that last ugly thing i wrote is what you get when you rationalize the numerator. yes now the h cancels.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0leaving \[\frac{1}{(\sqrt{x}\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now you can replace h by 0 since you will not be dividing by 0.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to get... \[\frac{1}{(\sqrt{x}\sqrt{x})(\sqrt{x}+\sqrt{x})}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[=\frac{1}{2x\sqrt{x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh damn i made a mistake early on the numerator was \[x(x+h)=h\] not \[xx+h\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a very bush league mistake but easily rectified. just replace the 1 in the numerator by 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the correct answer is \[\frac{1}{2x\sqrt{x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then don't forget to multiply by the 2 at the end because we factored it out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the "final answer" as we say is \[\frac{1}{x\sqrt{x}}\] sorry it took a while

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry my computer is freezing idk if its thes site or what

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sometime the site is funky. earlier today it certainly was.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you have a question about any step post and i will respond

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i understand thank you sooo much!
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