log sq root integral ln(√√x) dx

2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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Bijection of elements in tn & a pair of elements of (n+1)

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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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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd way: derivative (x^x)^x

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logic Idempotent law show x=xVx

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Pantun Melayu [Sorong papan tarik papan]

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lim x/e^x? as x→∞

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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Pantun Melayu [Buah cempedak di luar pagar]

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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Conversion: Permutation - Combination vice versa

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1st/4 ways: integral ∫1/(x + √x) dx

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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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

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UC Davis #14: integral ∫x √(4-x) dx

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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