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How would you use polar coordinates to solve this?


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Problem ID:                   6
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        AnSwEr0001: dne
        AnSwEr0002: 5
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A. lim(x,y)→(0,0)(x+12y)2x2+144y2= ___

B. lim(x,y)→(0,0)5x3+10y3x2+y2= ___

(Hint for B: use polar coordinates, that is x=rcos(θ),y=rsin(θ) )
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well,  I would substitute in the numerator and denominator the suggested coordinate transformation, and take advantage of the fact that the denominator takes an especially simple form, since x^2+y^2=r^2cos^2(θ)+r^2sin^2(θ) =r^2(cos^2(θ)+sin^2(θ))=r^2, and also of the fact that r->0 as (x,y)->(0,0).

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How do I find an integer for this problem?
Problem ID:                   6
Source file:                  Local/Dartmouth/setStewartCh15S3/problem_6.pg
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Number of incorrect attempts: 12
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The gas law for a fixed mass of an ideal gas at absolute temperature T, pressure P, and volume V is PV= mRT, where R  is the gas constant. Find the partial derivatives

∂P∂V=____

∂V∂T=____


∂T∂P=____


∂P∂V∂V∂T∂T∂P================   =
=______ (an integer) 
∂P∂V∂V∂T∂T∂P=         
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Well, it looks like you correctly computed the individual partial derivatives, so all you need to do is to multiply them together, and then maybe to substitute the ideal gas law back into the product so you can cancel everything except an integer constant
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I got the answer for most parts, but don't understand why the lim along the
y-axis is 0. I am not sure how to get the lim along the line. I have
guessed multiple times, but am unsure what to do with the constant.

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Well, x=0 on the y-axis, so the value of the numerator is 0 while the value of the denominator is 5y^2; in other words the value of the function on the y-axis is 0 except at the origin, where it is undefined. Since the limit of zero is zero, we're done.