Approximating a Function The table lists several measurements gathered in an experiment to approximate an unknown continuous function
x | 0.00 | 0.25 | 0.50 | 0.75 | 1.00 |
Y | 4.32 | 4.36 | 4.58 | 5.79 | 6.14 |
x | 1.25 | 1.50 | 1.75 | 2.00 |
y | 7.25 | 7.64 | 8.08 | 8.14 |
Approximate the
Using the Trapezoidal Rule and Simplson’s Rule.
Use a graphing utility to find a model of the form
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Chapter 8 Solutions
Calculus (MindTap Course List)
- aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).arrow_forwardRate of Change from Data Suppose f=f(x) satisfies f(2)=5 and f(2.005)=5.012. Estimate the value of dfdx at x=2.arrow_forwardDistanceWhen data are given in tabular form, you may need to vary the size of the interval to calculate the area under the curve. The next two exercises include data from Car and Driver magazine. To estimate the total distance travelled by the car in feet during the time it took to reach its maximum velocity, estimate the area under the velocity versus time graph, as in the previous two exercises. Use the left endpoint for each time travel the velocity at the beginning of that interval and then the right endpoint the velocity at the end of the interval . Finally, average the two answers together. Calculating and adding up the areas of the rectangles is most easily done on a spreadsheet or graphing calculator. As in the previous two exercises, you will need to multiply by a conversion factor of 5280/3600=22/15, since the velocities are given in miles per hour, but the time is in seconds, and we want the answer in feet. Source : Car and Driver. Estimate the distance traveled by the Chevrolet Malibu Maxx SS, using the table below. Acceleration Seconds Zero to 30mph 2.4 40mph 3.5 50mph 5.1 60mph 6.9 70mph 8.9 80mph 11.2 90mph 14.9 100mph 19.2 110mph 24.4arrow_forward
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- Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table. t (sec) v (ft/s) 0 21 10 35 20 37 30 35 40 35 50 35 Estimate the distance traveled by the vehicle during this 50-second period using the velocities at the beginning of the time intervals.distance traveled ≈ feetGive another estimate using the velocities at the end of the time periods.distance traveled ≈ feetarrow_forwardFind the average value of the function f(x)=x2−21 on [0,6]. Question content area bottom Part 1 The average value of the function f(x)=x2−21 on [0,6] is enter your response here.arrow_forwardSpeedometer readings for a vehicle (in motion) at 15-second intervals are given in the table. t (sec) v (ft/s) 23 15 24 30 24 45 19 60 24 75 30 Estimate the distance traveled by the vehicle during this 75-second period using the velocities at the beginning of the time intervals. distance traveled a feet Give another estimate using the velocities at the end of the time periods. distance traveled a |feetarrow_forward
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