NYU: 3 ways ∫(1+ln(x))/x dx

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Review: Linear form, Quadratic form & Bilinear form

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Pantun Melayu [Sorong papan tarik papan]

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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Lamar U: Use log. differentiation to find the 1st derivative of the given function

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prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.

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prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.

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If pv^a=C (where a & C are constant) find dv/dp & d2v/dp2

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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.

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multivariable Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1)...

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A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.

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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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AP Calculus: log ∫√x(√√x) da

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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Columbia U: 3rd way Evaluate the indefinite integral ∫1/(1+e^x) dx

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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