2010 Raytheon MATHCOUNTS National Competition

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derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

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derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

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

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

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

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

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Pantun Melayu [Sorong papan tarik papan]

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Pantun Melayu [Sorong papan tarik papan]

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

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

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

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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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AP Calculus 2nd way trig ∫sin^3(x)/(cos(x)-1) dx

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AP Calculus 2nd way trig ∫sin^3(x)/(cos(x)-1) dx

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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2 ways: Evaluate lim sin(x)/tan(x) where x tends to 0.

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2 ways: Evaluate lim sin(x)/tan(x) where x tends to 0.

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2nd/2ways: Taylor series of sin(x)

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2nd/2ways: Taylor series of sin(x)

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2nd/2ways: Taylor series of cos(x)

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2nd/2ways: Taylor series of cos(x)

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Screen Recording 2024-02-16 at 8.23.14 PM

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Screen Recording 2024-02-16 at 8.23.14 PM

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2024 MIT Integration Bee Final

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2024 MIT Integration Bee Final

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

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Screen Recording 2024-02-22 at 10.23.21 PM

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Screen Recording 2024-02-22 at 10.23.21 PM

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U Arizona: 2nd way For each integral decide which of the following is needed: ...

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U Arizona: 2nd way For each integral decide which of the following is needed: ...

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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