
Concept explainers
(a)
The upper and lower estimate of the total quantity of the oil that has escaped after 5 hours.
(a)

Answer to Problem 28E
The upper estimate is 758 gal and the lower estimate is 543 gal.
Explanation of Solution
Given information:
Formula used:
Add the leakages and multiply with unity because length of subinterval is unity.
Calculation:
For upper estimate after 5 hour take the value of leakage from time equal to 1 up to 5, Then Add the leakages and multiply with unity because length of subinterval is unity.
For lower estimate after 5 hour take the value of leakage from time equal to 0 up to 4, Then Add the leakages and multiply with unity because length of subinterval is unity.
Conclusion:
The upper estimate is 758 gal and the lower estimate is 543 gal.
(b)
The quantity of the oil that has escaped after 8 hrs.
(b)

Answer to Problem 28E
The upper estimate is 2363 gal and the lower estimate is 1693 gal.
Explanation of Solution
Given information:
Formula used:
Add the leakages and multiply with unity because length of subinterval is unity.
Calculation:
For upper estimate after 8 hour take the value of leakage from time equal to 1 up to 8, Then Add the leakages and multiply with unity because length of subinterval is unity.
For lower estimate after 5 hour take the value of leakage from time equal to 0 up to 4, Then Add the leakages and multiply with unity because length of subinterval is unity.
Conclusion:
The upper estimate is 2363 gal and the lower estimate is 1693 gal.
(c)
The number of hours that will elapse in the worst case before the oil has been leaked.
(c)

Answer to Problem 28E
The time taken will be 32.37 hours.
Explanation of Solution
Given information:
Formula used:
The time taken is determined by dividing the leakage with time.
Calculation:
In the worst case,
In the best case,
Conclusion:
The time taken will be 32.37 hours.
Chapter 6 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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