1 and 2 are solve for integral3. A bucket weighing 2 kg and a rope of negligible mass is used to draw water from a well that is 40.8 meters deep. Just before the bucket starts being raised from the bottom of the well, the bucket is filled with 6 kg of water. Unfortunately, there is a hole in the bucket and water leaks out at the rate of 0.12 kg per second. The bucket is pulled up at a constant rate of 0.8 meters per second.(a) How much water is in the bucket when the bucket reaches the top of the well?(b) Find the work done pulling the bucket to the top of the well.(Assume that the acceleration of gravity is 9.8 meters per second per second.4. For each series, determine whether it converges or diverges.Indicate clearly which test you are applying. You do not need to evaluate the series.Question 1, 2 and 4a 4b are in the file attached
m252_quiz3_duemay17sp19.pdf
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Math 252: take home quiz (due May 17, 2019)
Name:
Z
dx
√
1.
x2 + 16
Z
2.
t2
√
dt
t2 − 16
3. A bucket weighing 2 kg and a rope of negligible mass is used to
draw water from a well that is 40.8 meters deep. Just before the
bucket starts being raised from the bottom of the well, the bucket is
filled with 6 kg of water. Unfortunately, there is a hole in the bucket
and water leaks out at the rate of 0.12 kg per second. The bucket
is pulled up at a constant rate of 0.8 meters per second.
(a) How much water is in the bucket when the bucket reaches the
top of the well?
(b) Find the work done pulling the bucket to the top of the well.
(Assume that the acceleration of gravity is 9.8 meters per second
per second.)
4. For each series, determine whether it converges or diverges.
Indicate clearly which test you are applying. You do not need to
evaluate the series.
(a)
(b)
∞
X
n2 + 1
√
n6 + 9
n=1
n
∞
X
2n − 1
n=1
n2 + 1
…
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