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

UC Davis: differentiate y=2^cot(x)

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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

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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx

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integral exp ∫e^(mx)/(x^n) dx via Reduction formula

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2024 #3 MIT Integration Bee Final Lightning Round

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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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Variability or spread of a distribution. Whey we need it!

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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Columbia U: 1st way integral ∫√(x^2-9)/x^4 dx

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Why the mean of AP is the median of AP? mean=median?

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NYU: 3 ways ∫(1+ln(x))/x dx

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#3 UC Davis integrate ∫3/(4+x^(1/3)) dx via power sub

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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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Show integral x/(x^2+a^2) dx = -1/(2(x^2+a^2))

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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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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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Evaluate integral cos(2x)/(sin(x)+cos(x))^2

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