Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anjali_pant Group Title

Let f(x,y)=2xy/(x^2+y^2)^1/2 (x,y) not equal to (0,0) , f(0,0)=0 Show fyx(0,0) not equal to fxy(0,0) using method fxy= lim k->0 [ fx(0,k)-fx(0,0)]/k fyx=lim h->0 [ fy(h,0)-fy(0,0)]/h

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    umm, this may be stupid, but how can the function be defined for (0,0) when it already says (x,y) not equal to (0,0). [read second line of the problem] am i missing something?

    • 2 years ago
  2. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Well nothing is stupid . Thats how you prove limits. Google it !

    • 2 years ago
  3. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah i know limits, but then you must mean in the second line that lim f(0,0) = 0 x,y->0 right??

    • 2 years ago
  4. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yup !

    • 2 years ago
  5. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    What does fx(0,k) mean? x->0 and y -> k?

    • 2 years ago
  6. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But f(0,0) isn't defined, is it?

    • 2 years ago
  7. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Maybe @dumbcow knows how to do it, this stuff is a little advanced for me. I'm fairly certain this isn't a complicated problem, but I haven't taken multi-variable calculus yet.

    • 2 years ago
  8. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    okay so i seem to think fxy here is partial differential of f(x,y) wrt to x, and fyx is partial differential of f(x,y) wrt to y. see the structure. and same here, haven't taken advanced calculus, so don't think i ll be able help much other than guessing.

    • 2 years ago
  9. dumbcow Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    interesting, i find that fxy = fyx , im assumimg these are second partial derivatives \[\large f_{xy} = f_{yx} = \frac{6x^{2}y^{2}}{(x^{2}+y^{2})^{5/2}}\] http://www.wolframalpha.com/input/?i=d%2Fdx+d%2Fdy+2xy%2Fsqrt%28x^2%2By^2%29 http://www.wolframalpha.com/input/?i=d%2Fdy+d%2Fdx+2xy%2Fsqrt%28x^2%2By^2%29

    • 2 years ago
  10. dumbcow Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    since they are equavalent, the limit at (0,0) would also be the same

    • 2 years ago
  11. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah i logically was also getting that conclusion, but ofcourse more based on logical guessing and less of calculations.

    • 2 years ago
  12. dumbcow Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe the question was show they are equal ?

    • 2 years ago
  13. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    may be yes. high chances of that.

    • 2 years ago
  14. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The question is that show they are not equal. I stated the method to be used , and that's the way I have to do it in my exam , and not just simple estimation.

    • 2 years ago
  15. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Actually its a "step by step" sort of way , but I was not able to prove the conclusion , maybe some logical error Iam facing.

    • 2 years ago
  16. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    lets try this first off we need \(f_x(x,y)=\frac{2y^3}{(x^2+y^2)^{\frac{3}{2}}}\)

    • 2 years ago
  17. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    and so \(f_x(0,y)=\frac{2y^3}{(y^2)^{\frac{3}{2}}}=2\) if i am not mistaken

    • 2 years ago
  18. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    well hold on this is symmetric in x and y, so why these would not be the same is now confusing me. hmmm

    • 2 years ago
  19. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Read the following link. Complete the steps, then mimic for your function http://www.unf.edu/~omilatov/MAC2313/differentiability.pdf

    • 2 years ago
  20. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @ satellite , the method Iam talking about , you are not following that , maybe thats what misleading you !

    • 2 years ago
  21. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @elias, I know the steps , its that Iam not able to prove the inequality , some logical error that too in the last steps are over shadowing the ans ! So see if you could solve it step by step

    • 2 years ago
  22. Zarkon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I would check to make sure that you wrote down/typed the correct function

    • 2 years ago
  23. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yup the function is correct , i copied directly from my book .

    • 2 years ago
  24. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and its sort of a proof , and not just straightforward estimation of fxy or fyx , maybe thats why many are getting confused !

    • 2 years ago
  25. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Those two limits seem to be both infinite.

    • 2 years ago
  26. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[ f_x(x,y)=\frac{2 y^3}{\left(x^2+y^2\right)^{3/ 2}}\\ f_y(x,y)=\frac{2 x^3}{\left(x^2+y^2\right)^{ 3/2}} \] You can show from the definition that \[ f_x(0,0)= f_y(0,0)=0\] so \[\frac{ f_x(0,k) - 0}{k}=\frac{2}{\sqrt{k^2}} \] and \[\frac{ f_y(k,0) - 0}{k}=\frac{2}{\sqrt{k^2}} \]

    • 2 years ago
  27. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So the limit when x tends to zero is infinite for both.

    • 2 years ago
  28. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yea even I was getting the same ans ! but since the ques demands something different , I got stuck in between ! Then I thought since its coming to be infinity , so it must be implying that limits does not exist !

    • 2 years ago
  29. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes.

    • 2 years ago
  30. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    pardon ?

    • 2 years ago
  31. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Do not worry about it.

    • 2 years ago
  32. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    From May its my papers , so have a reason to worry ! :-(

    • 2 years ago
  33. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    i think there is something wrong here because this function is symmetric in x and y, i.e. if you replace x by y and y by x you get the same thing. so why one should be different from the other is not at all clear to me

    • 2 years ago
  34. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :-(((((( no idea ! :-(((((

    • 2 years ago
  35. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Both limits diverge to \[ \infty \] In a way they are not different.

    • 2 years ago
  36. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    They are not different , but does not exist either !

    • 2 years ago
  37. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes.

    • 2 years ago
  38. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Iam gettting your point , infact I myself concluded the same ans , but ques says something else. I ll confirm it tomorrow and will let you know. Thanks a lot for your help ! :-)

    • 2 years ago
  39. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    phew... please don't forget to confirm what this was all about!

    • 2 years ago
  40. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    lol ! Yea this method is a bit "mugging up" thing , maybe you have never read that, so you were getting confused so as to what to do ! Anyways google it ,its a proper method ! And yea thanks ! :-)

    • 2 years ago
  41. apoorvk Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    definitely mugging up method i believe. atleast very theoretical or subjective. bet it's for a theory paper in your uni, right?

    • 2 years ago
  42. anjali_pant Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    actually maths is a subsi in my course ! But yea it must be there in maths(h) ! IMP PROOOF ! :P

    • 2 years ago
  43. eliassaab Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Please read http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives The above problem is a bit related to the link above

    • 2 years ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.