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2nd/3 parts: Growing patterns

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logic: tautology p→q≡(¬q→¬p)
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logic: tautology p→q≡(¬q→¬p)

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logic Idempotent law show x=xVx
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logic Idempotent law show x=xVx

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integral ∫ x dx withOUT using Power rule.
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integral ∫ x dx withOUT using Power rule.

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e
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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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2nd way: integral ∫ log √x(x^n) dx
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2nd way: integral ∫ log √x(x^n) dx

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Pantun Melayu [Buah cempedak di luar pagar]
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Pantun Melayu [Buah cempedak di luar pagar]

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

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Simplify the following statements using only the connectives ∧, ∨ and ¬
2:58

Simplify the following statements using only the connectives ∧, ∨ and ¬

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1st/2 ways: derivative y=(ln(x))^x
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1st/2 ways: derivative y=(ln(x))^x

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#8 2021 MIT Integration Bee Qualifying Exam
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#8 2021 MIT Integration Bee Qualifying Exam

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Winx club: The Magic Is Back S1 Ep1- A new fairy in Alfea
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Winx club: The Magic Is Back S1 Ep1- A new fairy in Alfea

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2 ways: Σ 1? where k=m to n
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2 ways: Σ 1? where k=m to n

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2nd way: Find dy/dx a)x^y=y^x b)x^y+y^x=(x+y)^(x+y c) (cos(x))^y=(sin(y))^x
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2nd way: Find dy/dx a)x^y=y^x b)x^y+y^x=(x+y)^(x+y c) (cos(x))^y=(sin(y))^x

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2nd way: integral ∫1/(a + √√b (x^2)) dx
2:15

2nd way: integral ∫1/(a + √√b (x^2)) dx

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1st/2 parts: Inverse 2x2 matrix
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1st/2 parts: Inverse 2x2 matrix

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Compute the arithmetic mean for the following grouped data ...
3:42

Compute the arithmetic mean for the following grouped data ...

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sq root log derivative √ ln(f(x))
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sq root log derivative √ ln(f(x))

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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)
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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)

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prob stat: Show if y=ax+b where a & b are constants then ȳ = ax̄ + b
2:37

prob stat: Show if y=ax+b where a & b are constants then ȳ = ax̄ + b

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1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture
3:41

1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

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