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4 ways: Evaluate Σ(2k+1) k=1,20
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(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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sq root derivative √'(f(x)
1st/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2
trig integral ∫x sec^5(x^2) tan(x^2) dx
Think about the SS values you might obtain if you computed SS for these 22 samples...
2 ways: Show log b^(1/n)(a) = n logb(a)
trig Show (sec(x)+1)/sec^2(x) = sin^2(x)/(sec(x)-1)
exp integral ∫ (e^2x -1) /(e^2x +1)dx
Simplify the Boolean function F=A+A'B
The number of solutions of the equation x^(log10(x)) = 100x
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4th/4parts: Maclaurin Series [ahp kia]
UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n
Camping & Masak EP 1 season 2
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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))
3 ways: derivative log(x+ (1+√(x^2)))
trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)
2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'