Unformatted text preview: he same slope as the tangent line.
Its slope is rise/run = (ycomponent)/(xcomponent) = 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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This document was uploaded on 03/05/2014 for the course MAT 193 at CSU Dominguez Hills.
 Fall '11
 GeorgeJennings
 Calculus

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