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Tram L.

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Basic Math

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Question:

68 : 4 = ? 17 * 5 = ? 11^2 = ?

Tram L.

Answer:

1, 17 2, 85 3, 121

Calculus

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Question:

Calculate the first derivative of function f given by f(x)= (x^1/2 + 2x) * (4x^2-1)

Tram L.

Answer:

f'(x) = (1/2 * x ^ -1/2 +2) * (4x^2 - 1) + (x^1/2 + 2x) * (8x) = 2*x^3/2 + 8*x^2 - 1/2*(x^-1/2) - 2 + 8*x^3/2 + 16*x^2 = 24* x^2 + 10 * x^3/2 - 1/2*(x^-1/2) -2

Algebra

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Question:

If a^2 - b^2 = 8 and a*b = 2, find a^4 + b^4

Tram L.

Answer:

a^2-b^2=8 -> (a^2-b^2)^2 = a^4 + b^4 - 2*a^2*b^2= 8^2 =64 (1) a*b=2 -> 2*a^2*b^2=8 (2) Substitute (2) into (1) -> a^4 + b^4 = 64 + 8 = 72

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