# Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 15

Limit $l$ does not exist.

#### Work Step by Step

Consider $l=\lim\limits_{(x,y) \to (0,0)} \dfrac{y}{x^2-y}$ Suppose $y=p x^2$; $p \ne 1$ Now, $l=\lim\limits_{(x,y) \to (0,0)} \dfrac{y}{x^2-y}=\lim\limits_{(x,px^2) \to (0,0)} \dfrac{px^2}{x^2(1-p)}$ Thus, $l=\lim\limits_{(x,px^2) \to (0,0)} \dfrac{px^2}{x^2(1-p)}=\dfrac{p}{1-p}$ Hence, the limit $l$ does not exist as we can see that $l$ will have different limit for different values of $p$.

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