Matthew S.

Engineering Student at Vanderbilt University

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Linear Algebra

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Question:

Find the image of T: R^2 -> R^3 defined by T(x) = Ax and A = [1 0] [2 3] [4 3]

Matthew S.

Answer:

im(T) = span{a, b} where a = [1] and b = [0] [2] [1] [4] [1]

Calculus

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Question:

Find an implicit solution to dy/dx = (y+2)(y+3).

Matthew S.

Answer:

S 1/[(y+2)(y+3)] dy = S 1 dx S [ 1/(y+2) + -1/(y+3) ] dy = x + C ln(abs((y+2)/(y+3))) = x+C (y+2)/(y+3) = C(e^x)

Calculus

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Question:

Find the analytical antiderivative of f(x) = (e^x) * sin(x)

Matthew S.

Answer:

S (e^x)sin(x)dx = -(e^x)cos(x) + S (e^x)cos(x)dx + C = -(e^x)cos(x) + (e^x)sin(x) - S (e^x)sin(x)dx + C This implies: S (e^x)sin(x)dx = (1/2)(e^x)(sin(x) - cos(x)) + C

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