Limit in Two variables.

  • Thread starter smatik
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  • #1
smatik
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1

Homework Statement



lim (x,y)[itex]\rightarrow[/itex](0,0) f(x,y)=2*x/(x[itex]^{2}[/itex] + x +y[itex]^{2}[/itex])

Homework Equations



used different paths like y=k*x ,where k is a constant and y=k*x^2

The Attempt at a Solution


Got an answer 2 but solution says does not exist. Can anybody convince me that why limit does not exist,without using polar form.

I am currently studying in 1st year of college.
 

Answers and Replies

  • #2
haruspex
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The problem with the paths you chose is that there is one direction you are unable to represent with a finite k. What direction do you think that would be?
 
  • #3
smatik
14
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oh got it thanks man. its the y axis!! The limit comes out to be zero if i put x=1. Thanks!
 

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