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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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#8 2021 MIT Integration Bee Qualifying Exam

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Bijection of elements in tn & a pair of elements of (n+1)

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Qimiao Mengke Season 5 Episode 24 "Come Back, Bubble Mengke"

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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2nd/3ways: exp Derivative x^x

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#17 2022 MIT Integration Bee Qualifying Exam

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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2 ways: integral ∫ (4t+7) dt

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2 ways: derivative x √√x

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

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A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.

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Show that ar sinh(x) = ln(x + √ (x^2+1))

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examples: 2x2 matrix which is its own inverse

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sq root derivative √x [Good to know the result]

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trig integral a) ∫csc^2(x) dx

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Find the Maclurin series for (2x+3)(5x-4)

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integral ∫(x^2+2x)/(x^2+2x+2) dx

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Alternate way: trig integral ∫sin(x) dx

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