Multivariable Calculus Quiz
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MULTIVARIABLE FUNCTIONS
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Consider the function f(x,y)=x2yx4+y2f(x,y) = \frac{x^2 y}{x^4 + y^2}. A student calculates the limit of f(x,y)f(x,y) as (x,y)→(0,0)(x,y) \to (0,0) along any line y=mxy=mx and finds that lim⁡x→0f(x,mx)=0\lim_{x \to 0} f(x, mx) = 0 for all real numbers mm. Based on this information, what can be concluded about lim⁡(x,y)→(0,0)f(x,y)\lim_{(x,y) \to (0,0)} f(x,y)?
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