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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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2nd/3ways: trig integral ∫sec(x) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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2nd way: integral ∫ log √x(x^n) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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Logical equivalent involving ... tautology & contradiction
alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
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integral ∫(x^2-x+1)/(x^2+x+1) dx
2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".
Which of the following statements are true, & why?
Derivative 1) tanh(ln(x)) 2) (x^2-1)/(x^2+1)
2nd/2parts: Linear interpolation (2 given points)
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Growing patterns #2
4 ways: trig integral ∫sin(x) cos(x) dx
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