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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