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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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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))
3 ways: Derivative x^(-1/x)
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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
1st/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2
3 ways: derivative log(x+ (1+√(x^2)))
5 ways: trig Derivative of sin^2(x)
NUS MA1102R: For f(x,y) = e^(xy) + x/y, compute fx & fy
trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula
trig integral ∫x sec^5(x^2) tan(x^2) dx
2nd Alt. way: log Taylor series of ln(sec(x)) withOUT Taylor series explicitly
4 ways: Evaluate Σ(2k+1) k=1,20
NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)
2 ways: trig integral ∫tan^3(x) sec^2(x) dx
2 ways: Show log b^(1/n)(a) = n logb(a)
Which of the following data sets has a median of 3?
Think about the SS values you might obtain if you computed SS for these 22 samples...