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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=
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Pantun Melayu [Buah cempedak di luar pagar]
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1st way: exp ∫(e^x)/x (1+x log(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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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trig Write each expression as an equivalent algebraic expression involving only x.
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Review: Linear form, Quadratic form & Bilinear form
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Swinburne U 2nd way: e^(-e^x) e^x dx
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Pantun Melayu [Sorong papan tarik papan]
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Median [special weighted mean]
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1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2
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2 ways: ∫1/(x^2+2x-3) dx
prpob stat A bag contains 5 black balls 6 red balls. Determine the number of ways in which ...
1st/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2
integral ∫x^3/(x+2) dx
5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number
Lamar U 2nd way: evaluate integral ∫√(1+2ln(7x))/2 +10x^3/(x^4 +9) dx
Lamar U: Use log. differentiation to find the 1st derivative of the given function
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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]
Rutgers U: Verify using calculus