Results 1 to 3 of 3

Thread: continuity problem

  1. #1
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355

    Question continuity problem

    how to check the continuity of the function defined by:-
    $\displaystyle f(x,y) = \frac{sin(x^2y)}{x^2+y^2} , if (x,y)\neq(0,0)
    =0 , if (x,y)=(0,0)$
    at (0,0)?

    i think it should be done by using polar transformation, but can not do it. any help is appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,801
    Thanks
    3035
    You know that $\displaystyle x= r cos(\theta)$, $\displaystyle y= r sin(\theta)$, and $\displaystyle r^2= x^2+ y^2$, don't you? So, in polar coordinates, your function is $\displaystyle f(r,\theta)= \frac{sin(r^3 sin^2(\theta)cos(\theta)}{r^2}$

    Why didn't you write that at least?

    Now, $\displaystyle sin(\theta)$ and $\displaystyle cos(\theta)$ are always less than 1 so $\displaystyle sin(r^3 sin^2(\theta)cos(\theta))< sin(r^3)$. What can you say about the limit, as r goes to 0, of $\displaystyle \frac{sin(r^3)}{r^2}$?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    i did try that earlier here http://www.mathhelpforum.com/math-he...tml#post574521, but nobody replied. (thanks for your help in that thread)

    whatever, leave it. here $\displaystyle \frac{sin(r^3)}{r^2} = r\frac{sin(r^3)}{r^3}$. now, as $\displaystyle n-->\infty,$ we get $\displaystyle 0*1 = 0$ is it correct?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity problem help..
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Jun 2nd 2010, 10:56 AM
  2. Continuity Problem
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Mar 28th 2010, 05:08 PM
  3. Continuity problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Jan 27th 2010, 04:20 AM
  4. Continuity problem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Nov 30th 2009, 03:48 PM
  5. Continuity Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 20th 2009, 02:15 PM

Search Tags


/mathhelpforum @mathhelpforum