How can we show that the limit of the following surface integral is finite?
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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.
calculus limits multivariable-calculus vectors surface-integrals
asked Nov 15 at 11:36
Joe
395113
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up vote
1
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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.
calculus limits multivariable-calculus vectors surface-integrals
asked Nov 15 at 11:36
Joe
395113
What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
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.
calculus limits multivariable-calculus vectors surface-integrals
asked Nov 15 at 11:36
Joe
395113
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.
calculus limits multivariable-calculus vectors surface-integrals
calculus limits multivariable-calculus vectors surface-integrals
asked Nov 15 at 11:36
Joe
395113
asked Nov 15 at 11:36
Joe
395113
edited Nov 15 at 12:16
asked Nov 15 at 11:36
Joe
395113
asked Nov 15 at 11:36
Joe
395113
asked Nov 15 at 11:36
Joe
395113
395113
What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16
add a comment |
What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16
What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16
add a comment |
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What is $hat{r}$?
– AlgebraicallyClosed
Nov 15 at 12:07
$hat {r}$ is a unit vector from our surface to origin.
– Joe
Nov 15 at 12:16