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Unformatted text preview: Fall 2006 M408C Test #3 McAdam SHOW YOUR WORK. ANSWERS WITHOUT WORK GET NO CREDIT.
Points: 1) 3O 2) 10 3) 30 4) 10 5) 20
PLEASE PUT YOUR DISCUSSION SECTION TIME ON THE FRONT COVER. 1) Find the following anti—derivatives. a) ,lx‘V2x2+1dx b) ix4x+ldx c) gigEarl; dx
2) The two curves shown here are y = 7 — X2 and y = x2  1. Find the area of the shaded region. 3) One Fall day you park your car at mile marker 5 on a straight highway.
You take your bike from the trunk, and start pedaling. Let us take t = 0 to be your starting time (t in hours). At time t = 3, you get a ﬂat tire on your bike, and so have to walk back to
your car. Suppose at timet (with 0 s t s 3) your speed was V(t) = 3t2 — 18t + 24 = 3(t  2x: — 4).
(Positive speed indicates increasing mile markers.) a) How many miles did you bike, before the flat?
b) How far must you walk to reach your car? 0) What is the highest mile marker you reached? 4) Chicago already has 3 inches of snow on the ground. A new snow storm
starts at 1 o'clock and lasts until 3 o'clock. During the storm, the rate of snow accumulation it causes is r(t) 2 2t — (l/t2) inches/hour. For 1 s t s 3, find a formula for the amount of snow on the ground at time t. 5) It starts to rain at one o'clock (t = 1). At time t 2 l, the rate of rainfall is r(t) : 3t2 + 1 inches per hour. You have an open can in your backyard
which is collecting the rain. The can is 35 inches high, and already had 7
inches of water in it when the rain started. a) At what time does the can become filled up. (Assume the rain lasts long
enough to fill the can.) b) At time t = 2, how fast is the water level in the can raising.
(This is the easiest problem on the test! Think about the reality of what
is happening.) ...
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 Fall '08
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