MATH 1150

Midterm 2 | Spring '13 | Dupre

1. An eagle is coasting in a horizontal circle, by making use of updrafts. The circle has a radius of 50 feet and the eagle moves around this circle with a constant speed of 20 feet per second. What is the eagle’s acceleration in feet per second per second?

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2. Suppose that $f, g : \mathbb{R} \to \mathbb{R}$ are both smooth functions and that $f(5) = 3, g(5) = 2, f(2) = 4, g(3) = 7, f'(5) = 4, g'(3) = 2, f'(2) = 6, g'(5) = 10$ Calculate $(f - g)'(5)$.

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3. Calculate $(fg)'(5)$.

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4. Calculate $(f \circ g)'(5)$.

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5. Calculate $(g \circ f)'(5)$.

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Calculate $(f/g)'(5)$.

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Calculate $f'(x)$ if $f : \mathbb{R} \to \mathbb{R}$ is $f(x) = \frac{x^5 - 8}{x^4 + 2x^2 + 3}$

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8. Suppose $g : \mathbb{R} \to \mathbb{R} \backslash \{ 0 \}$ and $f : \mathbb{R} \to \mathbb{R}$ are smooth functions with $f' = f$ and $g' = g$. If $h = (f/g)$, what is $h'(2)$?

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