## University Calculus: Early Transcendentals (3rd Edition)

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