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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.
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logic: tautology (¬p→q)∧(¬p→¬q) →p
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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]
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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))
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prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.
Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2
derivative log f(g(x)) (a)
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2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))
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logic: tautology p→q≡(¬q→¬p)
Evaluate the integrals
rational function integral x/(x-√(x^2-1)) dx
1st/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)
2nd/2ways: r-Permutations
1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture
1st/2ways: Evaluate trig integral ∫1/(sin(x)+cos(x)) dx
3rd/10parts: Exclusive disjunction
2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx
trig integrals ∫cot(ax+b) dx vs ∫cot^2(ax+b) dx
2 ways: integral ∫(x-a)/(x+a) dx
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