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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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
Transcribed Image Text:There are two coloured pencils: red and blue. The tip of the red pencil is
moving along the x-axis and the tip of the blue pencil is moving along the y-axis. The
locations of the tips of the red and blue pencils at timet are given by differentiable
functions r(t) and b(t), respectively. We know that r(t) = sin(t) – 2. However, we know
only that the tip of the blue pencil moves along the positive y-axis with b(0) = b'(0) = 1.
We are interested in the areas of the triangles made by the two tips of the pencils and
the origin. Let's denote such an area at time t by A(t). For example, at t = 0 the area
is equal to A(0) = 1. (Check this to make sure you understand the question!).
Find the formula for A(t) in terms of r(t) and b(t). You may want to
(a)
make sure that your formula gives A(0) = 1.
(b)
Find the rate of change of the area when t = 0.
Expert Solution
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