# Chapter 13 - Section 13.2 - Limits and Continuity in Higher Dimensions - Exercises - Page 691: 46

The limit does not exist

#### Work Step by Step

Consider $f(x,y)=\dfrac{x^2-y}{x-y}$ Let us consider the approach: $(x,y) \to (0,0)$ along $y=mx; m\ne 1$ Then, we get $\lim\limits_{x \to 0}\dfrac{x^2-mx}{x-mx}=\dfrac{-k}{1-k}$ This shows us that there are multiple limit values when the approach is different and therefore, the limit does not exist for the given function.

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