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L'Hopital's rule for more than one variable?

  1. Feb 26, 2009 #1
    Is there an analog to l'Hopital's rule for functions of more than one variable? Or am I stuck using [itex]\epsilon[/itex] [itex]\delta[/itex] proofs and the squeeze theorem? Those also depend on me knowing the value of the limit beforehand which can be tricky in itself.
    Last edited: Feb 26, 2009
  2. jcsd
  3. Feb 26, 2009 #2


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    lim f/g=lim {[D_n]f}/{[D_n]g}
    where D_n is the directional derivative in the direction of the limit
    [D_n]f=dx fx+dy fy
    where fx and fy are partial derivatives
    lim (x,y)->0 sin(x^2+y^2)/(x^2+y^2)=lim cos(x^2+y^2)(2xdx+2ydy)/(2xdx+2ydy)=1
    or in polar form
    lim r->0 sin(r^2)/(r^2)=lim cos(r^2)(2r.dr)/(2r.dr)=1
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