My Homework - Can You Help Me?

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ozgunozgur

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I am trying to solve these questions for hours :/
 

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This is a help site, not an answer site.

Please read

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Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com

You have managed to ignore several of the requirements for this site at one fell swoop.

With respect to your first problem, let's start by defining a "critical point." What is your definition?
 
JeffM said:
This is a help site, not an answer site.

Please read

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com

You have managed to ignore several of the requirements for this site at one fell swoop.

With respect to your first problem, let's start by defining a "critical point." What is your definition?
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I did question 2. Is it true? Can you help me?
 

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No, neither attempt at #2 is right. In the first, you misinterpreted [MATH]e^y^8[/MATH] as [MATH]\left(e^y\right)^8[/MATH]. In the second, you changed the order of integration without adjusting the limits. Try that again, after sketching the region.
 
Dr.Peterson said:
No, neither attempt at #2 is right. In the first, you misinterpreted [MATH]e^y^8[/MATH] as [MATH]\left(e^y\right)^8[/MATH]. In the second, you changed the order of integration without adjusting the limits. Try that again, after sketching the region.
Click to expand...

Thanks. I am going to deal with it now. Do you help me solve it by your text? So is third question true, sir?
 
Can you review my answer?
 

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For #3, you never finished, as far as I can see. I would have used polar coordinates.

Please confirm the problem in #2. Is that an 8 or a 3? And are you sure the limits are stated correctly? I'm referring to the original problem.
 
Dr.Peterson said:
For #3, you never finished, as far as I can see. I would have used polar coordinates.

Please confirm the problem in #2. Is that an 8 or a 3? And are you sure the limits are stated correctly? I'm referring to the original problem.
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Can't you write? I'm not that good. :/
 
These are my answers. Can you review them?
 

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For #3, you found x and y in polar form for points on the boundary (the circle), not throughout the region. So that doesn't work at all.

If you want to follow my suggestion of using polar coordinates, then you need to express x^2 + y^2 in terms of r and theta for any point on the plane, and express dA in terms of polar coordinates. If you haven't learned that, then stick with rectangular coordinates. In that case, you'll need to determine the limits of integration from the equation of the region.

For #2, you seem to have changed the 8 to a 3; can you show us a better image of the problem so we can confirm that. But in any case, the limits of integration seem wrong to me; the inner integral, with respect to x, should not have x in its limits! So I suspect that the problem is just wrong, unless you're being taught a notation different from what I know. But you seem to be interpreting it in the only way that makes sense, and your new limits are almost right. Sketch the region and make a small correction. This will also make the second integral work better.

I don't know what your notation means; it looks like r(...) and Or(...), and I don't know what they could mean that would be reasonable. Are they some special functions you've been taught?
 
Dr.Peterson said:
Please confirm the problem in #2. Is that an 8 or a 3? And are you sure the limits are stated correctly? I'm referring to the original problem.
Click to expand...

These questions were also posted on another site on which I participate, and one of our staff surmised the problem is supposed to be:

[MATH]I=\int_0^1 \int_{\sqrt x}^1 \exp(y^3)\,dy\,dx[/MATH]
I have shown the OP how to reverse the order of integration to obtain:

[MATH]I=\int_0^1\int_0^{y^2} e^{y^3}\,dx\,dy[/MATH]
And have asked if they can proceed.
 
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