# How can we show that the limit of the following surface integral is finite?

I have an arbitrary parameterized surface $$S(u,v)$$ in Cartesian coordinates (with finite area) and the surface passes through origin. There is a very small circular hole of radius $$\epsilon$$ at the origin.

Is there a way to show that the limit of the following surface integral is finite? $$\displaystyle \vec{V} = \lim \limits_{\epsilon \to 0} \iint_S \dfrac{dS}{r^2} \hat{r}$$ Here $$r$$ is the distance between origin and points on our parameterized surface $$S(u,v)$$. $$\hat {r}$$ is a unit vector from our surface to origin.

• What is $\hat{r}$? – DrinkingDonuts Nov 15 '18 at 12:07
• $\hat {r}$ is a unit vector from our surface to origin. – Joe Nov 15 '18 at 12:16