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Math Help - Finding the points where a function is continous

  1. #1
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    Finding the points where a function is continous

    Find the set of all points of continuity for:

    f(x,y) = ln(\frac{x-y}{x^2+y^2})

    i know that the domain is whenever ln is positive, so its whenever x-y>0 , x>y

    is it continuous on all points of the domain?
    also is it considered continuous on the edges of the surface?

    thanks
    Last edited by travelalfred; March 9th 2010 at 09:35 PM.
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  2. #2
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    function is continuous everywhere

    Quote Originally Posted by travelalfred View Post
    Find the set of all points of continuity for:

    f(x,y) = ln(\frac{x-y}{x^2+y^2})

    i know that the domain is whenever ln is positive, so its whenever x-y>0 , x>y

    is it continuous on all points of the domain?
    also is it considered continuous on the edges of the surface?

    thanks
    f(x) is said to be continuous when lim(x->a+)f(x)=lim(x->a-)f(X)=f(a).
    where a is any point in the domain.
    following a similar analogy for your 2 variable function i think f(x,y)is continuous everywhere as f(a,a)=0=lim(x->a+-)lim(y->a+-)f(x,y) in the domain which means that all the points of continuity will lie in the
    domain. and the domain is given by whenever x>y for all reals.
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  3. #3
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    Quote Originally Posted by travelalfred View Post
    Find the set of all points of continuity for:

    f(x,y) = ln(\frac{x-y}{x^2+y^2})

    i know that the domain is whenever ln is positive, so its whenever x-y>0 , x>y

    is it continuous on all points of the domain?
    also is it considered continuous on the edges of the surface?

    thanks
    Since the "edge of the surface", x= y, is NOT in the domain, the question of whether the function is continuous there is moot- it is not even defined threre!
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    Quote Originally Posted by travelalfred View Post
    Find the set of all points of continuity for:

    f(x,y) = ln(\frac{x-y}{x^2+y^2})

    i know that the domain is whenever ln is positive, so its whenever x-y>0 , x>y

    is it continuous on all points of the domain?
    also is it considered continuous on the edges of the surface?

    thanks

    Re-write it as ln(x-y) \, - \, ln(x^2+y^2).

    Looks easier, Right?
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