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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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logic: tautology (¬p→q)∧(¬p→¬q) →p
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Pantun Melayu [Sorong papan tarik papan]
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Bijection of elements in tn & a pair of elements of (n+1)
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stat: SLR Properties of residuals
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#12 2024 1st/2ways: MIT Integration Bee Qualifying Exam
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一个平静却让人深思的英文故事 | 沉浸式听觉体验 (English Story)
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4 ways: trig integral ∫tan(x) dx
prob stat: The following frequency table gives the values obtained
A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R
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2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2
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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
2nd way: ∫1/(√(1-x^2)(1+arc sin(x))^2) dx