pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

Pantun Melayu [Sorong papan tarik papan]

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2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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Conversion: Permutation - Combination vice versa

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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alternate way: count sum 1+3+5+ ... +(2n-1)

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2nd/3part: Maclaurin Series [ahp kia]

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2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'

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2 ways: diff eq Solve dy/dx-x^2=0

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OSU Math 1151 Practice1: Compute the derivative (1)-(8)

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