anjilaghimire anjilaghimire
  • 07-04-2017
  • Mathematics
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[tex] \lim_{(x,y) \to \ (0,0)} (x^4 +y^3)/(x^4 + y^2) [/tex]

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LammettHash
LammettHash LammettHash
  • 07-04-2017
If [tex]x=0[/tex], you have

[tex]\displaystyle\lim_{y\to0}\frac{y^3}{y^2}=\lim_{y\to0}y=0[/tex]

But if [tex]y=0[/tex], you have

[tex]\displaystyle\lim_{x\to0}\frac{x^4}{x^4}=\lim_{x\to0}1=1[/tex]

So the limit does not exist.
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