Solving Multivariable Limit: Find Limit or Show No Existence

[Laura1321412]

Homework Statement

Find that the limit exists, or show that the limit does not exist.

lim (x,y) --> (0,0) of (x^2 * sin^2y)/(x^2 + 2y^2)

Homework Equations

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The Attempt at a Solution

i used the lines x=0 y=0 and both times got the limit 0 so i attempted to prove the limit exists

I attempted to use the limit definition,

1 >= |sin^2| >= 0
x^2 + 2y^2 >= x^2
x^2+2y^2 >= x^2sin^2y
|x^2sin^2y/x^2+2y^2| <= 1

uhmm... I am not sure what do after this or really what the heck I am doing. HELP? :)

 

[number0]

You are forgetting to check one last condition before proving that the limit exist! Not sure if it would do anything but try plugging x = y and y = x. If this checks out ( = 0) then you can be sure that the limit exist and try to prove it.