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Problem 16

When we estimate distances from velocity data, it…

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Problem 16

When we estimate distances from velocity data, it is sometimes necessary to use times $ t_0, t_1, t_2, t_3, ... $ that are not equally spaced. We can still estimate distances using the time periods
$ \Delta t_i = t_i - t_{i-1} $. For example, on May 7, 1992, the space shuttle $ Endeavour $ was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table, provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height above the earth's surface of the $ Endeavour $, 62 seconds after liftoff.
Problem 17

The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.
Problem 18

The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period.
Problem 19

In someone affected with measles, the virus level $ N $ (measured in number of infected cells per mL of blood plasma) reaches a peak density at about $ t = 12 $ days (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of $ N(t) $ from
$ t = 0 $ to $ t = 12 $ (as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells x time). The function $ N $ has been modeled by the function $$ f(t) = -t(t - 21)(t + 1) $$

Use this model with six subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms of measles.
Problem 20

The table shows the number of people per day who died from SARS in Singapore at two-week intervals beginning on March 1, 2003.

(a) By using an argument similar to that in Example 4, estimate the number of people who died of SARS in Singapore between March 1 and May 24, 2003, using both left endpoints and right endpoints.

(b) How would you interpret the number of SARS deaths as an area under a curve?
FL
Frank L.
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32
Problem 15

Oil leaked from a tank at a rate of $ r(t) $ liters per hour. The rate decreased as time passed and values of the rate at two-hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.

Answer

$L_{5}=70$liters$, R_{5}=63.2$liters

Chapter 5
Integrals
Section 1
Areas and Distances
Calculus: Early Transcendentals

Topics

Areas and Distances

Discussion

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Video Transcript

here, give you the oil leaking rate and ask you to find the finds. Ah, it's a total amount of oil that leaks out so again the time into those two hours. And what is the lower estimate? The lower estimate for each in time interval we use the smallest possible e great Assauer estimate so far is that from zero to two, we pick seven point six against the table. It's on your textbook. From two to four. We pick a six point eight six point two from six to eight. We put five point seven from eight to ten. We pick five points. Three a simile for up her ah each interval pictures the largest leaking rate for for our estimate and each time into those two hour. By the way, the unit's leader here and so the first one should be a point seven. The second one seven point six six point eight six point two five point seven

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