[Multivariable Calculus] Flux and Maple Program

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Homework Statement

It would help if you guys had access to Maple
Anyways here is the problem: http://poibella.org/calc3f11/wp-content/uploads/2011/09/lab_3_vector_calc_F_11.pdf
It is on question 12 asking for flux and the questions after that.

Homework Equations

In the link

The Attempt at a Solution

So for the s and t ranges I got -0.01..0.01 for both of them. Also on the graph imagine a plane that spans from -0.04 to 0.04 on the y axis, -0.01 to 0.01 on the z axis and x=4. Someone told me to compute the cross product of the length of the sides, and then dot it with <4,-3,0>. However I'm not sure if this is correct when finding flux.
From there, how do i answer question 13 and 14?

 

[mighty2000]

Hi there,

Thank you for sharing your problem with us. In order to solve this problem, it would be helpful to have access to Maple, as it is a powerful computational tool that can assist with calculations and graphing. However, if you do not have access to Maple, there are other ways to solve this problem.

First, make sure you have correctly determined the ranges for s and t. It seems like you have correctly determined them to be -0.01 to 0.01 for both s and t. Next, it is important to visualize the problem in three dimensions. Use the given graph to imagine a plane that spans from -0.04 to 0.04 on the y-axis, -0.01 to 0.01 on the z-axis, and x=4. This will help you better understand the problem and how to approach it.

To find the flux, you will need to compute the cross product of the length of the sides, and then dot it with <4,-3,0>. This is because flux is defined as the flow of a vector field through a surface. In this case, the vector field is given by <4,-3,0>, and the surface is the plane defined by the given ranges for s and t. Therefore, by computing the cross product of the length of the sides, you are finding the area of the surface, and then by dotting it with the vector field, you are finding the flow of the vector field through that surface.

To answer question 13, you will need to use the formula for flux, which is given by the dot product of the vector field and the normal vector to the surface. The normal vector to the surface can be found by taking the cross product of the tangent vectors to the surface. Once you have the normal vector, you can plug it into the formula and solve for the flux.

For question 14, you will need to use the formula for the divergence of a vector field, which is given by the dot product of the gradient of the vector field and the normal vector to the surface. Again, you will need to find the normal vector to the surface by taking the cross product of the tangent vectors. Once you have the normal vector, you can plug it into the formula and solve for the divergence.

I hope this helps guide you in solving this problem. If you need further clarification or assistance, please don't hesitate to ask. Good luck!