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**1. Homework Statement**

From here, question C.

http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx

[itex] lim (x,y) -> (0,0) \frac {x^2y^2}{x^4 + 3y^4} [/itex]

**2. Homework Equations**

**3. The Attempt at a Solution**

So if we approach along the x axis, we know y will be 0, so we get

[itex] lim (x,0) -> (0,0) \frac {x^2(0)^2}{x^4 + 3(0)^4} [/itex]

[itex] lim (x,0) -> (0,0) \frac {x^2(0)^2}{x^4 + 3(0)^4} [/itex]

After applying direct substitution after this, the reason they get the answer 0, and not undefined, is because the limit is APPROACHING zero, meaning its not actually getting evaluated there, and since they got 0 on the numerator, they get zero? Because if we apply direct substitution it will be undefined, but since its the limit its not actually zero is an infinitely close value to zero?