calc 3 help

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Of course...in calc and stuff all these geometric figures are surfaces.fixitmattman wrote:Points A and B aren't on the surface of the sphere (B will be somewhere in it though), but everything that's 1:2 in length from A:B respectively is. I'm assuming all the points it maps are going to be on the surface/outside radius of the sphere.
Yeah, this would definitely help. Of course, this assumes that the described points form a sphere, but this will get us the center and radius.fixitmattman wrote:Obviously you're going to need to plot out a bunch of points that meet the 2:1 ratio. You should be fine with plotting out where the octants will be. Hint that top octant will be at 2:1 between A and B giving you the colinear segment APB, where the other will be colinear to that line, but will be in the order ABP. This will give you the 'top' and 'bottom' octant points of the sphere. Knowing these two points will allow you find the center and the radius. Then you can find the rest of the octants and once you have them will have to check that they all conform to a distance of 2 from A and 1 from B, and they probably will seeing as how it says so.
The (very) hard part about this problem is showing that the points described do, in fact, form a sphere. The only way I can think of is to come up with an equation for the described figure that looks like
(x  h)^2 + (y  k)^2 + (z  l)^2 = r^2
and coming up with that involves quite a bit of trig and some nasty drawings.
Edit: The above equation is that of a sphere with center (h, k, l) and radius r.
Or perhaps you could find the center and the radius (r) as described above and show that all the points described are equidistant from the center with distance r. That would also become quite involved, though. Unfortunately, I don't have the time to get into this.
Are you into numerical analysis, or are you just doing it as a course for a science/engineering program? NA can be pretty cool once you get into it...but it can also be quite challenging. I just hope that you know Taylor's theorem very well...fixitmattman wrote:If that doesn't help, I could do up a sketch for you, but I'm busy dealing with my hell known as Numerical Analysis. Right now Matlab is teh gay. The big thinker was I thought it would plot inbetween A and B, but it doesn't.
 fixitmattman
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Numerical is a core class I have to take. After that I think I'm going to run far far away.
I haven't done Taylors theorem at all, which sucks because it's popping up everywhere. Trying to deal with that now too.
I haven't done Taylors theorem at all, which sucks because it's popping up everywhere. Trying to deal with that now too.
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How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done
How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done
Man...that sucks! Taylor's theorem is where tons of numerical methods come from. Basically, you can write any function as a power series centered at a point x0 by finding its derivatives at that point:
f(x) = f(x0) + f'(x0) (xx0) + [f''(x0)/2!] (xx0)^2 + ... + [f^(n)(x0)/n!] (xx0)^n + [f^(n+1)(a)/(n+1)!] (xx0)^(n+1)
with a strictly between x and x0.
The last term is the remainder term, and its analysis is important to characterize the error of a method. The first n terms are used to develop the method.
I'm sure you'll see how cool it is to come up with things like Newton's method for finding zeros, Euler's method for integrating ODEs, and various difference formulas for approximating the first and second derivative of a function.
f(x) = f(x0) + f'(x0) (xx0) + [f''(x0)/2!] (xx0)^2 + ... + [f^(n)(x0)/n!] (xx0)^n + [f^(n+1)(a)/(n+1)!] (xx0)^(n+1)
with a strictly between x and x0.
The last term is the remainder term, and its analysis is important to characterize the error of a method. The first n terms are used to develop the method.
I'm sure you'll see how cool it is to come up with things like Newton's method for finding zeros, Euler's method for integrating ODEs, and various difference formulas for approximating the first and second derivative of a function.
 fixitmattman
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The derivatives I can handle and for the most part I can usually find the expression for the sequence. It's the remainder term I'm still working on. For now I've been able to squeak by through referencing a table of presolved Taylor series.
We were supposed to learn it in my last vector calculus class, but it ended up getting left for last and pretty much ignored. Now all of a sudden it's everywhere.
This is why I drink.
We were supposed to learn it in my last vector calculus class, but it ended up getting left for last and pretty much ignored. Now all of a sudden it's everywhere.
This is why I drink.
http://www.cardomain.com/profile/fixitmattman
How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done
How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done
 fixitmattman
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 Posts: 1930
 Joined: Sun Jul 24, 2005 10:05 pm
 Location: North York
Uh yeah, speaking of that, when do the girls start showing up anyways
http://www.cardomain.com/profile/fixitmattman
How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done
How to fix your car:
1. Buy a Haynes manual
2. Read Haynes maual
3. Read and search appropriate threads, trust us, it's been covered before
4. Fix car
5. Consume beer of job well done