8 Views PremiumSep 22, 2023
UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
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🪔 Happy Deepavali 🪔 [Nov-12-2023]
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Review: Linear form, Quadratic form & Bilinear form
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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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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logic: tautology (¬p→q)∧(¬p→¬q) →p
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integral ∫ x dx withOUT using Power rule.
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alternate way: count sum 1+3+5+ ... +(2n-1)
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#9 2010 MIT Integration Bee Qualifying Exam
alternate way: count sum 1+2+3+ ... +n
review Differentiation [Implicit]
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Conversion: Permutation - Combination vice versa
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3rd/3ways: trig integral ∫sec(x) dx
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3rd/3 ways: trig integral ∫ sin(ax+b) dx
2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'
#1 2021 MIT Bee Qualifier: trig integral sin(x) cos(x) tan(x) sec(x) csc(x) cot(x) dx
Alternate way: trig integral ∫sin(x) cos(x) cos^7(2x) dx ... Just in 1 line.
Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx