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Matthew B.

Chemical Engineering student at the University of Waterloo

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Linear Algebra

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Question:

Find the vertical and horizontal asymptotes of the function f(x) = (x-2)/(x^2-16).

Matthew B.

Answer:

The vertical asymptote can be found by making the denominator equal to zero and solving for x. x^2-16 = 0 x = 4, -4 Therefore there is a VA at x = 4 and x = -4 The horizontal asymptote can be found by looking at the highest exponent of x, which in this case if x^2. Looking only at that term we find 0/1 = 0. Therefore there is a HA at y = 0.

Chemistry

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Question:

Complete the missing parts of the following sentence. During photosynthesis water undergoes __________ while carbon dioxide undergoes ________.

Matthew B.

Answer:

The answer to this question is: During photosynthesis water undergoes OXIDATION while carbon dioxide undergoes REDUCTION. This is because water loses electrons while carbon dioxide gains electrons.

Calculus

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Question:

What is the tangent line of the function f(x) = 2x^3-4x^2-3x at x = 2?

Matthew B.

Answer:

First we must take the derivative to find the tangent slope at x = 2 f'(x) = 6x^2-8x-3. f'(2) = 6(2)^2-8(2)-3 = 5 Now we must find the y intercept of the tangent line f(2) = 2(2)^3-4(2)^2-3(2) = -6 Using y=mx+b -6 = 5(2)+b b = -16 Therefore the tangent line of the function at x = 2 is y = 5x-16

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