Screen Recording 2024-03-03 at 12.03.07 AM

Solve the differential equation xcos^2(y) dx + tan(y) dy=0

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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2nd way: integral ∫ log √x(x^n) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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2 ways: sq root derivative 1/(√√(1/√x))

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lim x/e^x? as x→∞

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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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set Show X∩ ((Y∪ X') ∩ Y') = ∅

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*Screen Recording 2024-05-05 at 11.12.45 PM

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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3

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Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?

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1st/2 ways: derivative y=(ln(x))^x

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integral ∫√(x-a)/x dx

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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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2nd way: derivative y=e^x sin(x) cos^3(x)

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Screen Recording 2024-02-02 at 1.54.05 AM

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prob stat: A die with 4 red faces & 2 green faces is rolled twice.

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AP Calculus 2nd way:

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U Penn: Show that the following decomposition CANNOT hold ...

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