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I'm a bit lost on how to calculate and graph what the prompt is asking me for. If someone could provide some direction, that would be fantastic!

Using the data provided, estimate the total change in the object.

1. Use a right-endpoint estimate.

2. Use a left-endpoint estimate to approximate the total change of the object.

3. Calculate the best estimate for the total change of the object.

4. Graph the model using the behavior of the functions represented by the data.

5. Discuss the relevance of the solution and how this graph represents it, using the calculus terminology of curve sketching. (Is the graph decreasing or increasing? How is this related to the data presented?)

Calculate Parts I and II.

A. Using the the model for each set of data, calculate the acceleration of the object using rules for differentiation.

B. Using the model for each set of data, calculate the total change of the object using rules for integration.



Table I
t in seconds 0 5 10 15 20 25 30 35 40 45
v(t) in mph 187 152.18 122.2 96.41 74.21 55.1 38.64 24.49 12.3 1.81

Table 2:
t in seconds 9 10 19 20 29 30 39 40 44 45
v(t) in mph 127.84 122.2 78.38 74.21 41.74 38.64 14.6 12.3 3.79 1.81

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[Guest]

To calculate the total change in the object using right-endpoint and left-endpoint estimates, you'll need to approximate the area under the velocity-time graph. The velocity-time graph represents the behavior of the object over time. Here's how you can proceed:

1. Right-endpoint estimate for total change:
For each interval between two consecutive time points, multiply the velocity at the right endpoint of the interval by the width of the interval (time difference between the two points), and then sum up these products for all intervals.

For Table 1:

Interval 1 (0-5 seconds): 152.18 mph * 5 seconds = 760.9 mph·s
Interval 2 (5-10 seconds): 122.2 mph * 5 seconds = 611 mph·s
... and so on for each interval until the last one.
Add up all these products to get the right-endpoint estimate for the total change.

2. Left-endpoint estimate for total change:
Similar to the right-endpoint estimate, but you use the velocity at the left endpoint of each interval instead.

For Table 1:

Interval 1 (0-5 seconds): 187 mph * 5 seconds = 935 mph·s
Interval 2 (5-10 seconds): 152.18 mph * 5 seconds = 760.9 mph·s
... and so on for each interval until the last one.
Add up all these products to get the left-endpoint estimate for the total change.

For Table 2, repeat the same process.

After calculating both estimates, you can discuss which one might provide a better approximation and why, considering the behavior of the function.

As for graphing the model, you'll be plotting the velocity-time graph provided by the data. This graph will show how the velocity of the object changes over time. You'll observe whether the velocity is increasing, decreasing, or remaining constant and how this behavior relates to the data presented.

In working through this mathematical problem, it's clear that precision and accuracy are key. For those seeking assistance or guidance with such calculations, I will suggest you to try mathsassignmenthelp website that can be incredibly valuable. Also, you can contact them at +1 (315) 557-6473.