anonymous
  • anonymous
2xy/3x+y What is answer when x limit zero & y limit zero ?????
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\lim_{x,y \to 0}\frac{2xy}{3x+y}\] divide by xy you get \[\lim_{x,y \to 0}\frac{2}{\frac{3}{y}+\frac{1}{x}}\]
anonymous
  • anonymous
we can now evaluate \[\lim_{y \to 0}\frac{3}{y}=\infty\] and \[\lim_{x \to 0}\frac{1}{y}=\infty\] hence we have \[\lim_{x,y \to 0}\frac{2xy}{3x+y}=\frac{2}{\infty}=0\]
anonymous
  • anonymous
thank u .....is it indeterminate form???

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anonymous
  • anonymous
@hartnn
hartnn
  • hartnn
yes, jonask ?
anonymous
  • anonymous
underterminate shud mean that we cant decide about the limit right for example \[\infty^\infty\] but here we know the limit is 0
anonymous
  • anonymous
so its derterminate
anonymous
  • anonymous
thanks lot
hartnn
  • hartnn
and hey, lahiru, \(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)
anonymous
  • anonymous
\[\Huge \color{purple} { WELCOME ,LAHIRU} !!!\]
Zarkon
  • Zarkon
what if you come along the path \[y=-\sin(3x)\]
Zarkon
  • Zarkon
\[y=-3\sin(x)\] is a little nicer.
Zarkon
  • Zarkon
Just to be clear...I'm saying the limit does not exist.

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