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review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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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Review: Linear form, Quadratic form & Bilinear form
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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 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
Why the mean of AP is the median of AP? mean=median?
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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
Black Far West - Une contre-histoire de l'Ouest
UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]
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Differentiate the function y= x^3 (1+x)^2 /((1-x)^4 (1+2x)^2)
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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?
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2nd way: trig integral ∫sin(a/x +b)/x^2 dx
The pth, qth, & rth terms of an AP are x,y,z respectively.
Show integral ∫x √(ax+b) dx = 2(3ax-2b)√(ax+b)^3 /(15a^2)
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UC Davis: differentiate y=ln(cos^5(3x^4))
UC Davis P#6: 2nd way differentiate y= (√x)^(√x) e^(x^2)