APPLICATIONS1. You are waiting at an intersection when the light turns green. Your car’s velocity as a function from the time the light turns green is given below. Find upper and lower bounds for the distance you traveled during the first 2.5 seconds.Time (sec) 0.0 0.5 1.0 1.5 2.0 2.5Velocity (ft/sec) 0 10 25 40 30 222. A log begins to lose weight after it is cut due to drying. If 1000( )w t dt represents the total weight loss (in pounds) due to drying over the first 100 days, what does ( )w t represent?3. Water is flowing into a reservoir at the rate of ( )r tgallons per hour. A. Give a practical interpretation of 40( )r t dt. B. Give an upper and lower bound for the total number of gallons of water that would flow into the reservoir during the first day if 2100( )1r tt. Use 100n . C. How often would the rate values need to be recorded so that the upper and lower bounds would be no more than 10 gallons apart? How many subdivisions would be needed?4. The density of trees in a particular rectangular plot of forest is given by ( )xmeasured in hundreds of trees per square mile. If xrepresents the number of miles from the eastern edge, set up a definite integral to represent the total number of trees in this plot.100 miles North400 mile5. The projected rate of oil production in the non-Communist countries up to the year 2020 is shown below. If this projection is correct, estimate the amount of oil that would be produced between 2000 and 2015. Determine the average rate of production during that time interval.0510152025301975 1985 1995 2005 2015yearstrillions of barrels per
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