Chapter 9 Quiz Solutions

Its slope is riserun y componentx component y tx

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Unformatted text preview: he same slope as the tangent line. Its slope is rise/run = (y-component)/(x-component) = y ′ (t)/x′ (t). Reason #2. Let f be a function whose graph coincides with the parametrized cirve. Then y (t) = f (x(t)). By the chain rule it follows that y ′ (t) = f ′ (x(t)) ∗ x′ (t). Therefore f ′ (x) = y ′ (t) x′ (t) where x = x(t). 3. Find the area inside the larger loop and outside the smaller loop of the polar curve r(θ) = 1/2 + cos(θ). Solution: See the figure below. The inside lo...
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