Results 1 to 4 of 4

Math Help - Determining continuity of a two variable equation?

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    32

    Determining continuity of a two variable equation?

    Here is the question...
    Determine the points (x,y), if any, at which f(x,y) is not continuous.
    a. f(x,y) = \frac{x-y}{1+x^2+y^2}

    b. f(x,y)=e^{x+y}+\sqrt{x+y}

    Can someone please solve these and explain to me how to go about solving them? Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,490
    Thanks
    1391
    Quote Originally Posted by Infernorage View Post
    Here is the question...
    Determine the points (x,y), if any, at which f(x,y) is not continuous.
    a. f(x,y) = \frac{x-y}{1+x^2+y^2}

    b. f(x,y)=e^{x+y}+\sqrt{x+y}

    Can someone please solve these and explain to me how to go about solving them? Thanks in advance.
    Are you assuming real values for x and y?

    If so, the first will be continuous everywhere.

    There can only possibly be a discontinuity where the denominator is 0.

    But 1 + x^2 + y^2 > 0 for all real x and y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    32
    Quote Originally Posted by Prove It View Post
    Are you assuming real values for x and y?

    If so, the first will be continuous everywhere.

    There can only possibly be a discontinuity where the denominator is 0.

    But 1 + x^2 + y^2 > 0 for all real x and y.
    Oh okay, that makes sense. What about the second one though, because if x+y is negative than the square root can't be taken, so I'm not sure what to do with that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,536
    Thanks
    1391
    <br />
f(x,y)=e^{x+y}+\sqrt{x+y}<br />
    x+y is continuous everywhere and so is e^x so e^{x+y} is continous everywhere. \sqrt{x} is continuous for all positive x (and "continuous from the right" at x= 0) so \sqrt{x} is continuous for all (x,y) such that x+y> 0. x+ y= 0 or y= -x is a line through (0,0) and (1,0) has 1+ 0> 0 so \sqrt{x+y} is continuous "above and to the right" of that line.

    f(x,y)= e^{x+ y}+ \sqrt{x+y} is continous for (x,y) "above and to the right" of the line y= -x and "continuous from above and to the right:" on that line.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 25th 2011, 04:26 AM
  2. Determining continuity
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 19th 2010, 05:49 AM
  3. Two-Variable Limit and Continuity
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 7th 2010, 03:02 AM
  4. Continuity of a 2 variable function
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 1st 2009, 12:05 PM
  5. Determining continuity of function.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 18th 2009, 05:51 AM

Search Tags


/mathhelpforum @mathhelpforum