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Show that the function u(x,y)=e^x cos(y) is harmonic in the x-y plane

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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

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exp Calculate ∫x^3 3^x dx via IBP

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prob stat: Find the expected value & std deviation in the number of '6's when 20 dice are rolled.

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5
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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1
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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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Lamar U 2nd way: evaluate trig integral ∫x sin(x^2) [cos^4(x^2) + 8 cos^2(x^2)-10] dx

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NYU: compute integral ∫√(1+ √x) dx

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.
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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?
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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx
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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx

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Laman utama>Show that the function u(x,y)=e^x cos(y) is harmonic in the x-y plane>