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Conversion: Permutation - Combination vice versa
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logic Idempotent law show x=xVx
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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Pantun Melayu [Buah cempedak di luar pagar]
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)
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What is π?
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx
1st/2 parts stat: SLR ∑ŷk = ∑yk where k=1,n
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2nd/2parts: Linear interpolation (2 given points)
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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100
4 ways: Evaluate Σ(2k+1) k=1,20
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Solve x(x-1)dy/dx - (x-2)y=x^3(2x-1) via Integrating Facto[IF]
2nd way: ∫(x+3)/(x^2+6x)^2 dx vs ∫(x+3)(x^2+6x)^2 dx
2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx
2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))
U North Texas Integration Bee 2nd way: x^2/√(x-1) dx
UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]