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

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Consider $P(x,y)=xy$ and the point $P(x,y) \to O(0,0)$ This means that $xy \to 0$ Plug in: $u=xy$ Now, $\lim\limits_{u \to 0}\dfrac{1-\cos u}{u}=\dfrac{0}{0}$, which shows the limit of Indeterminate form; thus, we will apply L-Hospital's rule: We get $\lim\limits_{u \to 0}\dfrac{\sin u}{(1)}=\sin (0)=0$