8 Views PremiumJun 21, 2023
2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2
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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
47 Views
logic: tautology (¬p→q)∧(¬p→¬q) →p
12 Views
2nd way: derivative (x^x)^x
25 Views
Pantun Melayu [Buah cempedak di luar pagar]
40 Views
Bijection of elements in tn & a pair of elements of (n+1)
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lim x/e^x? as x→∞
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
39 Views
MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
Conversion: Permutation - Combination vice versa
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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..
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2nd/2ways: count perm Show P(n,n)=P(n,n-1)
4 Views
UC Davis #14: integral ∫x √(4-x) dx
UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
3 Views
alternate way: count sum 1+2+3+ ... +n
1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number
alternate way: count sum 1+3+5+ ... +(2n-1)
2nd/3part: Maclaurin Series [ahp kia]
5 Views
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