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Exam 3A - playground and the town will pay half the cost of...

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Mt100 - Calculus I Exam 3 December 5, 2007 Variation: A On the cover of your blue book, put: your name your discussion section time: 10, 3, or 4 your test variation letter: above Put all your answers in the blue book. Be organized, clear, neat, and grammatically correct. Be concise, but be sure to show all your relevant work. The point value of each problem precedes it in parentheses. The total, of course, is 72. 1 . (24) Find dy dx . a. y = ln cos x ( ) b. y = x tan x c. y = e tan " 1 x d. xy = e y 2 2. (12) a. Use a linear approximation to estimate 32.1 5 . b. Find the linearization of A ( r ) = 4 " r 2 at a = 5 . 3 . (12) a. Find the local extrema of f ( x ) = 3 x 4 " 16 x 3 + 24 x 2 " 12 , and determine if they are local maxima, minima, or neither. b. Find the extreme values of g ( x ) = x " sin2 x on 0, " 2 # $ % % & ( ( .
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5 . (24) Do two, and only two, of the following. Begin each on a new page, with the problem choice clearly indicated. I. A man wants to put fencing that costs $10 a foot around a rectangular
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Unformatted text preview: playground, and the town will pay half the cost of that side. Find the dimensions (and area) of the plot of largest area that the man can afford. II. When a stone is dropped in a pool, a circular wave moves out from the point of impact at a rate of 6 inches per second. How fast is the area enclosed by the wave increasing when the wave is 4 " inches in circumference? III. The planet Vulcan is a large sphere, and the very logical inhabitants have measured the radius of their planet at 8126 kilometers. But with their typical precision, they understand that this measurement many be incorrect by as much as 10.7 kilometers. Estimate (with linear thinking) the possible error they will incur by using their measurement to calculate the volume of Vulcan....
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