A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
I am stuck with an easy problem  I must be missing something. I am trying to use the limit process to find the derivative of f(x) = 8 / sqrt of x. Can you help me see where I am messing up?
anonymous
 5 years ago
I am stuck with an easy problem  I must be missing something. I am trying to use the limit process to find the derivative of f(x) = 8 / sqrt of x. Can you help me see where I am messing up?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = 8/\sqrt{x}\] find the derivative using the limit process

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f'(x) = lim \[f^\prime(x) =\lim_{\Delta x \rightarrow 0} [(8/\sqrt{x+c} 8/\sqrt{x})/c]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am banging my head against this problem and getting a bad answer every time. We can tell by looking at it that the answer is\[(4/x^(3/2))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, I think you see what I mean...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But I haven't figured out the algebra to leave me with a 4 in the numerator. I keep getting stuck with things that don't work out in the end.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Weeku, what do you have for me so far?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Whoops, I made a mistake. Darn editor. . . Hold on.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Seems no matter what I try, I end up with delta x /[( sqrt x + delta x) + sqrt x]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am going in circles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah. I'm stuck as well. Hrm. . . I'm still trying, though. Sorry xD Interesting problem, though.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ah. Got it. Took a whole looseleaf paper to work out. . . Pretty nasty.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Did you get up to \[(8\sqrt{x}  8\sqrt{x+h}) / (h \sqrt{x}\sqrt{x+h})\]? Or, do you know how I got there? At that point, multiple the numerator and denominator by the conjugate of the numerator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Then it becomes a lot of distributing and factoring, until you can finally divide out the h. Once that happens, substitute 0 for h. Phew. I dunno if I can type out everything I did. . . I probably did it the long way, but I saw no other, shorter way. Do you want me to type it out?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, I got that far. I see you have h = delta x and you canceled out one h already.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would be grateful if you typed it out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Before that, all I did was find the common denominator of 8/sqrt[x+h] and 8/sqrt[x], add them together, and instead of dividing by h, multiply by 1/h to get \[8\sqrt{x}  8\sqrt{x+h} / h \sqrt{x} \sqrt{x+h}\] Then I factored out the 8 to get the above ^ Oh. Okay.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Whoops. Never mind about factoring out the 8.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I tried doing that, with no luck. :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\frac{8}{\sqrt{x+h}}  \frac{8}{\sqrt{x}}}{h}\]Firs Only the Numerator.... \[8\frac{\sqrt{x}  \sqrt{x+h}}{\sqrt{x+h}\times \sqrt{x}}\] Rationalization of Numerator \[\frac{8}{\sqrt{x+h}\times\sqrt{x}\times(\sqrt{x} + \sqrt{x+h})}\] \[\frac{8}{2\times x^{\frac{3}{2}}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ishaan94, I am looking over what you have done to see where I diverged. Thank you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I lost you after "Rationalization of Numerator," but nicely done. I did it the very, very long way, I see. . . Sorry about that, FreeTrader.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\Huge{\frac{\frac{8\cancel{h}}{\sqrt{x+h}\times\sqrt{x}\times(\sqrt{x} + \sqrt{x+h})}}{\cancel{h}}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[8\frac{\sqrt{x}  \sqrt{x+h}}{\sqrt{x} \times \sqrt{x+h}} \times \frac{\sqrt{x} + \sqrt{x+h}}{\sqrt{x} + \sqrt{x+h}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I see how Ishaan94 got to the "first only the numerator..." expression. But I am lost on how he got rid of the terms in the numerator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right, multiply by conjugate.

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0I really think you are going about this the wrong way. You should change the square root into a power (1/2) and then bring the denominator to the top by changing the power to negative. Then you can simply use the limit process of: f(x)= 8x^(1/2) f(x+h)=8(x+h)^(1/2) And plug this into the derivative formula. You should get rid of the terms in the denominator.

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0Then factor out a h and cancel.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[8\frac{x  (x+h)}{\sqrt{x}\times \sqrt{x+h} \times (\sqrt{x} + \sqrt{x+h})}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think it's dawning on me that I missed distributing the 1 on the h, too.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Stick with me, I am going to check that on my paper.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ishaan94, when I perform the operation 8 *[ x (x+h) ] I am left with 8x 8(x+h) which gives 8x 8x 8h

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which gives 8h. divide out the h's.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am onto this now... working the algebra. searching for the lightswitch for the bulb over my head...

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\frac{8}{\sqrt{x}}\] \[f(x)=\frac{8}{x ^{1/2}}\] \[f(x)=8x ^{\frac{1}{2}}\] \[f(x+h)=8(x+h)^{1/2}\] \[f \prime(x)\lim_{h \rightarrow 0}=I can't remember the formula\] Now just use you derivative formula, cancel where necisary, factor out a h, then cancel with the denominator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My problem is now in the denominator of the numerator. I don't see a h to cancel the one against the 8.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're forgetting that the entire equation is over h at this point. \[\Huge{\frac{\frac{8\cancel{h}}{\sqrt{x+h}\times\sqrt{x}\times(\sqrt{x} + \sqrt{x+h})}}{\cancel{h}}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have that now. Thanks. I am down to working with the remaining denom terms.

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0All terms on the right hand side of the minus sign in your derivative formula that have a x term should cancel with the terms. I think you're going about this the wrong way. Instead of having a quotient you should really bring the denominator to the top by making the power negative. Remember this rule? am^x = a/m^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes. I am already so deep in the prob that I am going to finish it with frax.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here's what I have in the denominator, which I am tempted to misspell as demonator. \[\sqrt{x} * \sqrt{x} * \sqrt{x+h} + \sqrt{x} * \sqrt{x+h} * \sqrt{x+h} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since the h values go to zero in the limit, the following is the denominator in the limit: \[2\sqrt{x}\sqrt{x}\sqrt{x}\]

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\frac{8}{\sqrt{x}}\] \[f(x)=\frac{8}{x ^{1/2}}\] \[f(x)=8x ^{\frac{1}{2}}\] \[f(x+h)=8(x+h)^{1/2}\] \[\lim_{h \rightarrow 0}f'(x)=\frac{f(x+h)f(x)}{h}\] lim{h>0) of f'(x) = (8(x+h)^(1/2)  8x^(1/2))/h You can do the rest, I'm sure.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, freetrader, (sqrt[x])^3 = x^(3/2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, I am losing my sanity. Can you help me remember if \[\sqrt{x^3} = \sqrt{x}\sqrt{x}\sqrt{x}\] ???

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0Yes  and this should be in the denominator of the equation once it has been solved. Notice how the ^(1/2) becomes 1.5 when you increase the power by one. And yes it does FreeTrader

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yup. That is a true statement.

chaise
 5 years ago
Best ResponseYou've already chosen the best response.0Stop writing it as a square root until you get to the final stage of the question. sqrt(x)^3 = x^(3/2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have temp insanity.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, my answer took me 7 hours to reach.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It was totally worth it!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.