UC Davis: differentiate y=(3x+1)^2

STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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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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logic Idempotent law show x=xVx

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Review: Linear form, Quadratic form & Bilinear form

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

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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Pantun Melayu [Buah cempedak di luar pagar]

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Pantun Melayu [Sorong papan tarik papan]

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

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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2 ways: Find logarithm of 5 to the base 5 √5.

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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logic: Simplify the Boolean function F=AB+(AC)'+AB'C(AB+C)

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UC Davis #1 2nd way: integral ∫1/(x^2-4) dx [integration by partial fraction]

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