integration bee 2014 UNSW 2nd way: tan(x)/(sin(x) cos(x)) dx

pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

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

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Pantun Melayu [Buah cempedak di luar pagar]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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sq root integral ∫1/√...√√x dx with n √

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Do you know ... paper folding ...

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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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2 ways: Find a formula for d/dx[f^m(x) g^n(x)], where f & g are differentiable functions ...

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Show log b^n(x^m) = m/n logb(x)

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"baby" fact: exp even odd e^x

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1st/3 parts: Growing patterns

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trig integral ∫1/(cos^2(a+bx) √(p^2-qtan(a+bx)) )dx

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2nd/2parts: Linear interpolation (2 given points)

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UC Davis #14: trig integral ∫(sin(x)-cos(x))(sin(x)+cos(x))^5 dx

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trig Show cos(4x) = 8 cos^4(x) -cos^2(x)+1

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sq root integral ∫1/√√x dx

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Vandermonde's Identity

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2 ways of "counting": 1=1/2+1/4+1/8+1/16+ ...

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2 ways: derivative ln(ax-b)^(p-qx)

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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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