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2 ways: integral ∫(x-a)/(x+a) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]
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When Wang Bian danced, the number of people in the live broadcast room soared from 5,000 to 20,000.
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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2
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matrix product: AB=0 where A≠0 & B≠0
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alternate way: count sum 1+2+3+ ... +n
examples: 2x2 matrix which is its own inverse
The water dance "Searching for Light" searches for abducted children, hoping that the light of hope
2 ways: Σ 1? where k=m to n
Robots are so cute and funny these days!
2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx
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trig integrals ∫cot(ax+b) dx vs ∫cot^2(ax+b) dx
2nd/2ways: count perm Show P(n,n)=P(n,n-1)
2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))
Vandermonde's Identity
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count comb: values nCn, nC(n-1), nC(n-2)
Find the number of subsets {1,{2,3}}