Possible title: Troubleshooting File Attachments on Online Forums

In summary, the two surfaces defined by xz^2 + 2yz +xy^2 = 4, 2x - 7y - 3z = 2 intersect in a curve S. Find the tangent line and normal plane to S at the point (3,1,-1).
  • #1
jameszy7
2
0
a) The two surfaces defined by xz^2 + 2yz +xy^2 = 4, 2x - 7y - 3z = 2 intersect in a curve S. Find the tangent line and normal plane to S at the point (3,1,-1).


b) Sketch the graphs of y = x^m and y = x^n where m and n are positive integers and x >= 0 . Find the area of the region enclosed between them. Is your answer valid for m>n or m <n ?

c) Let F = e^x i + 2ye^x j + e^2y^^2 k

(i,j and k are not part of the power)

Verify the divergence theorem over the box-like region described by
0<=x<=1, 0<=y<=2, 0<=z<=3.


d) Evaluate the triple integral

\int_{2}^{0} \int_{2x}^{0} \int_{y}^{0} xe^z dzdydx
Sorry if this looks messy, its my first post here :D
 
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  • #2
Hello jameszy7 and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
  • #3
Hi, Whenever I try to post something, it never works when I attach a document. I am not sure the reason to that.
 
  • #4
jameszy7 said:
Hi, Whenever I try to post something, it never works when I attach a document. I am not sure the reason to that.

What is the extension of the file, and the size of the file. We support certain file extensions and have a maximum size an attachment can be, which can be based on the file's extension.

What steps are you using to attempt to attach the file? What happens when you try to upload the file and/or submit your post? What kind of error message(s) do you receive?
 

Related to Possible title: Troubleshooting File Attachments on Online Forums

1. What is the purpose of evaluating multiple integrals?

The purpose of evaluating multiple integrals is to calculate the total value of a function over a certain region in multiple dimensions. This can be used in various fields of science, such as physics, engineering, and economics, to solve problems involving areas, volumes, and probabilities.

2. How do you set up a multiple integral?

To set up a multiple integral, you first need to determine the limits of integration for each variable. This is done by considering the boundaries of the region of integration and choosing the appropriate values for each variable. Then, you need to determine the order of integration, which can be done by considering the symmetry of the function or the ease of integration. Finally, you can write the multiple integral using the appropriate notation and the limits of integration.

3. What are the different types of multiple integrals?

There are two types of multiple integrals: double integrals and triple integrals. A double integral is used to calculate the volume under a surface in two dimensions, while a triple integral is used to calculate the volume under a surface in three dimensions. Double integrals are represented by two integral signs, while triple integrals are represented by three integral signs.

4. How do you evaluate multiple integrals?

To evaluate multiple integrals, you can use various techniques such as Fubini's theorem, change of variables, and integration by parts. Fubini's theorem states that the order of integration can be changed without affecting the final result. Change of variables involves substituting one or more variables with new ones to make the integration easier. Integration by parts is used to reduce a multiple integral into a single integral.

5. What are some real-life applications of multiple integrals?

Multiple integrals have various applications in different fields, such as calculating the center of mass and moments of inertia in physics, determining the probability of events in statistics, and finding the total cost and revenue in economics. They are also used in fluid mechanics to calculate the flow rate and fluid pressure in a given region, and in computer graphics to render 3D images and animations.

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