All Calculus 3 Resources
Example Questions
Example Question #1 :Line Integrals
Computefor
In order to find the divergence, we need to remember the formula.
Divergence Formula:
, where,, andcorrespond to the components of a given vector field.
Now lets apply this to our situation.
Example Question #5 :Line Integrals
Computefor
In order to find the divergence, we need to remember the formula.
Divergence Formula:
, where,, andcorrespond to the components of a given vector field.
Now lets apply this to our situation.
Example Question #6 :Line Integrals
Computefor
In order to find the divergence, we need to remember the formula.
Divergence Formula:
, where,, andcorrespond to the components of a given vector field.
Now lets apply this to our situation.
Example Question #7 :Line Integrals
Find, where
In order to find the divergence, we need to remember the formula.
Divergence Formula:
, where,, andcorrespond to the components of a given vector field.
Now lets apply this to our situation.
Example Question #1 :Divergence
Compute, where
All we need to do is calculate the partial derivatives and add them together.
Example Question #2 :Divergence
给定的向量场
find the divergence of the vector field:
.
Given a vector field
we find its divergence by taking the dot product with the gradient operator:
We know that, so we have
Example Question #1 :Divergence
Suppose that. Calculate the divergence.
We know,
使用这个来获得正确的答案
Example Question #2 :Divergence
Given that
calculate
using this formula we have
Example Question #1 :Divergence
Find, where F is given by the following curve:
The divergence of a vector is given by
where
So, we take the partial derivative of each component of our vector with respect to x, y, and z respectively and add them together:
The derivatives were found using the following rules:
,,
Example Question #6 :Divergence
Findwhere F is given by
The divergence of a curve is given by
where
Taking the dot product of the gradient and the curve, we end up summing the respective partial derivatives (for example, the x coordinate's partial derivative with respect to x is found).
The partial derivatives are:
The following rules were used to find the derivatives:
,
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