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December 1st, 2013, 07:11 AM  #1 
Newbie Joined: Dec 2013 Posts: 1 Thanks: 0  Some multivariable calculus problems
Here are some problems of multivariable calculus. https://www.dropbox.com/sh/vxpjv8wejpy0fb3/XJ3ulE7m85 Do anyone knows is answers? Just the answers will be fine, but with steps is even better if you are convinient. Many thanks. 
December 5th, 2013, 05:49 AM  #2 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: Some multivariable calculus problems
Summerleei, I hope you have the actual solutions to correct me where I have gone amiss. Here are my results 1.) The force field here is conservative, giving us that 2a.) For the ellipse, b.) 3a.) has the potential function , I don't think has any potential function, and has the potential function . b.) and Sorry, I was lazy to compute that for G because in applying Cauchy residues theorem, the denominator has double poles. c.) Green's Theorem may only be applied to the field F because the other two vector fields have singularities in the domain of integration. 4.) I didn't use Green's theorem for this one. (Can you please show me how to?) My result was . 5.) The flux is given by the formula Maximal flux occurs when . Maximal flux = 37632 6.) Flux equals . Flux from the bottom and top is zero because the gauss map to the object is orthogonal to the vector field on those portions. 

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