1st way: exp ∫(e^x)/x (1+x log(x)) dx

multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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2nd way: integral ∫ log √x(x^n) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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2 ways: sq root derivative 1/(√√(1/√x))

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lim x/e^x? as x→∞

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

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hello

XanderLao

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2nd/2 way: Expand e^sin(x) by Maclaurin's Theorem

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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2 ways: exp derivative a^(logb(cos(px+q))

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Let B be the mx1 col. matrix [1/m ... 1/m]'. If A =[a1 ... am] is any row matrix. What is AB?

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integral ∫(x^2+2x)/(x^2+2x+2) dx

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4th/4ways: trig derivative sin(x)

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Princeton U: trig integral ∫sin(x)/√(1+cos(x)) dx

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1st/4 ways: integral ∫1/(x + √x) dx

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2 ways: exp derivative ln(e^(x+1/x))

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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)

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3rd/3ways: Laplace Show that ...

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2nd/4ways: trig derivative sin(x)

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2 ways: sq root √x^x

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