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Conversion: Permutation - Combination vice versa
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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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🪔 Happy Deepavali 🪔 [Nov-12-2023]
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logic: tautology (¬p→q)∧(¬p→¬q) →p
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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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UC Davis #14: integral ∫x √(4-x) dx
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alternate way: count sum 1+2+3+ ... +n
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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
stat: SLR Properties of residuals
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alternate way: count sum 1+3+5+ ... +(2n-1)
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If sec(x+y)=xy then find dy/dx
review Differentiation [Implicit]
2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'
exp trig derivative x^x sin(x)
2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))
The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.
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