Center of gravity

Noismaker

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Hello, i have problems with understanding this exercises set theory:

E = {(x,y) ∈ R^2: x ≥ 0, |y| ≤ min{x^2, 2x − x^2}}.

the question are to draw the graph of E and in particular to understand how to determine |y| ≤ min{x^2 , 2x − x^2 }

Thanks for the attention.
 
Hello, i have problems with understanding this exercises set theory:

E = {(x,y) ∈ R^2: x ≥ 0, |y| ≤ min{x^2, 2x − x^2}}.

the question are to draw the graph of E and in particular to understand how to determine |y| ≤ min{x^2 , 2x − x^2 }

Thanks for the attention.
You have posted 3 problems without showing any work on your part! We do not know what you can do and where you would need help!
 
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Hello, i have problems with understanding this exercises set theory:

E = {(x,y) ∈ R^2: x ≥ 0, |y| ≤ min{x^2, 2x − x^2}}.

the question are to draw the graph of E and in particular to understand how to determine |y| ≤ min{x^2 , 2x − x^2 }

Thanks for the attention.

I think you're asking how to graph the inequality |y| ≤ min{x^2 , 2x − x^2 }.

I would start by graphing y = x^2 and y = 2x - x^2; then I'd use those to graph y = min{x^2 , 2x − x^2 }. There's more work to do after that, but perhaps you can show us how far you got in this process, so we can have a better idea what you need from us.
 
I think you're asking how to graph the inequality |y| ≤ min{x^2 , 2x − x^2 }.

I would start by graphing y = x^2 and y = 2x - x^2; then I'd use those to graph y = min{x^2 , 2x − x^2 }. There's more work to do after that, but perhaps you can show us how far you got in this process, so we can have a better idea what you need from us.

From this graph desmos-graph.jpg the question is how to determine the min{x^2 , 2x − x^2 }, or what is the algebraic procedure for the research of this minimum, independent of the use of the derivative.
This is an exercise assigned to the mathematics exam in the faculty of Chemistry.
Thank's
 
View attachment 9745
From this graph the question is how to determine the min{x^2 , 2x − x^2 }, or what is the algebraic procedure for the research of this minimum, independent of the use of the derivative.
This is an exercise assigned to the mathematics exam in the faculty of Chemistry.
Thank's

Just look at the graph! Which graph is below the other? For 0<=x<=1, x^2 is smaller, and for x>1, 2x-x^2 is smaller. That expresses the min as a piecewise-defined function. And since this is negative for x>2, you can consider only 0<=x<=2. That is the region that in your picture is sort of a dark orange.

Your mention of the derivative suggests you are misinterpreting the problem as being about finding the minimum of a function. No, it is just about finding which of two functions is smaller over a given interval.

Incidentally, your title was "Center of gravity", which suggests that you are subsequently asked to find the center of gravity of this region. Is that correct? That is where (integral) calculus will come in.
 
Just look at the graph! Which graph is below the other? For 0<=x<=1, x^2 is smaller, and for x>1, 2x-x^2 is smaller. That expresses the min as a piecewise-defined function. And since this is negative for x>2, you can consider only 0<=x<=2. That is the region that in your picture is sort of a dark orange.

Your mention of the derivative suggests you are misinterpreting the problem as being about finding the minimum of a function. No, it is just about finding which of two functions is smaller over a given interval.

Incidentally, your title was "Center of gravity", which suggests that you are subsequently asked to find the center of gravity of this region. Is that correct? That is where (integral) calculus will come in.

You have understood exactly the request, expressed in an English certainly not very technical and adequate of which I apologize.
In fact the next question was to determine the center of gravity of the region.
Thank you very much for your reply.
 
… what is the algebraic procedure for the research of this minimum …
If by "algebraic procedure" you're wondering how to find the minimum without using a graph, you could write the difference of the two functions and then construct a sign chart (to find intervals where the difference is positive or negative).

f1 - f2 > 0 means minimum is f2

f1 - f2 < 0 means minimum is f1

f1 - f2 = 0 means no minimum
 
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