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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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MP 2000 Hindustan: Evaluate β«(tan(x)+cot(x))^2 dx
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MPPET 1996 Hindustan: trig integral β« sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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2nd way: integral β« log βx(x^n) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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3 ways: Derivative x^(-1/x)
Example: Find the sum
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4 ways: Evaluate Ξ£(2k+1) k=1,20
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2 ways: diff eq Solve dy/dx-x^2=0
Determine the equation of the normal drawn to the astroid ...
Solve β(2x-5) -β(x-2) = 2
2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)
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Alternate way: Derivative y=ln((x^4-8)^5/(x^6+5x)cos(x))
2nd way: trig ππππππππ β«sin(x)cos(x)cos(4x)cos(8x)cos(16x)cos(32x)cos(64x) dx
trig integral β«sin^5(x) dx
2nd way: trig integral β«sin^6(ax+b) cos^6(ax+b) dx
2nd/2parts: Linear interpolation (2 given points)
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2 ways: sq root derivative 1/(ββ(1/βx))
A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.
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