Estimation is over or under estimate

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Homework Help Overview

The discussion revolves around the differential equation y'' = -y^2 and its implications for estimating the area under a curve. Participants are trying to determine whether a given approximation leads to an overestimation or underestimation of the exact area.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants question the relationship between the differential equation and the concept of area, with some seeking clarification on how to apply Riemann sums to approximate the area under a function. There is also a focus on determining the behavior of the function y(x) over a specified interval to assess whether it is increasing or decreasing.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the need to analyze the function's behavior to determine the nature of the approximation, but no consensus has been reached.

Contextual Notes

There is confusion stemming from the transition between the differential equation and the Riemann sum problem, as well as the lack of information about the function f(x) itself, which complicates the analysis of its increasing or decreasing nature.

dohsan
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Homework Statement


If y''=-y^2, is this approximationg an over-estimation or an underestimation of the exact area?


Homework Equations





The Attempt at a Solution

 
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Area of what? y''=(-y^2) is a differential equation. What does that have to do with an area?
 
I think this problem has to do with this equation... bc my teacher wrote it as a new problem and it confused me..

Write the Reimann sum that will approximate the area under the graph of the function y=f(x) that is continuous and positive over the interval [1,5] with n=8 using the right endpoint evaluation.
 
dohsan said:
I think this problem has to do with this equation... bc my teacher wrote it as a new problem and it confused me..

Write the Reimann sum that will approximate the area under the graph of the function y=f(x) that is continuous and positive over the interval [1,5] with n=8 using the right endpoint evaluation.

Ok, so to decide whether it is an overestimate or underestimate without actually solving the differential equation you need to at least decide whether y(x) is decreasing or increasing on [1,5]. Can you figure out how to do that?
 
Well, I believe you find y' which if f'(x), but not knowing what f is... it's quite confusing on how to find inc or dec on [1,5]. I just know if f'(x) > 0 .. it's inc.
 

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