Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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trig Write each expression as an equivalent algebraic expression involving only x.

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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2nd/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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commutative: ab=ba via "picture"

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4 ways: exp integral ∫a^(bx+c) dx

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Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)

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4 ways: derivative x(log(x)-1)

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2nd way: trig integral ∫1/(cos(x)(1+cos(x)) dx

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3 ways: derivative e^y=x

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1st/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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5 ways: trig derivative tan(x).

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cos(arc sin(x))? & tan(arc sin(x))?

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