Curves Definition and 778 Threads

so according to relativity, gravity is rly curves in space time. I imagine this in a 2d context, with a 2d world wrapped around a "balloon". Gravity would be like pushing in part of the balloon. If you think about the way this curvature distorts "quantized" space-time, it makes sense that...

Can anyone point me towards an online link or some books where I can study these bad boys? I am supposed to write like a 5-10 page paper on Peano curves in which I prove a few interesting things regarding them.

Find the area of the region bounded by the curves y=x , y=1/(x^2) , and x=2 I know after you sketch it you have to take the intergral of the top function minus the bottom function from the points that they intersect. I am stuck however because one function does not appear to be on top...

Hi, I'm doing a project which involves parametric curves that I have to present to a class. Basically, I'm completely exercises and I know that most computer-aided design works with parametric curves, specifically Bezier curves. For the project, I'd like to draw something in CAD or whatever and...

i have to show how many times the curves intersect at the origin y^4 = x^ 3 and x^2y^3 - y^2+ 2x^7= 0 i don't really know how to start solving this :rolleyes:

Hi, I'm having some trouble determining the formulae for banked curve problems, could somebody give me a general guideline on how to tackle these type of problems. My main problem is resolving the Normal reaction in terms of the angle of the inclined plain. Like i know that Ncos(angle) =...

I'll be honest, I don't understand most of what's going on in this forum, so forgive me if this isn't the right place. I'm trying to extrapolate a quadratic curve between two points (my x values). These are known, as are the corresponding y values and the y' (or dy/dx if you prefer) values...

How do I prove that two curves are orthogonal when they interest each other at a specific point? Do I just take the derivative of both and compare the slopes? The slopes should be negative reciprocals of each other, correct?

I'm kinda stuck on this question... my text gives me a simple example, but it's far from enlightening. Just wondered if I could get some help! "At what point on the curve y = 1 + 2e^x - 3x is the tangent line parallel to the line 3x -y =5?" Would I just need to simply compare the slopes...

Find the area bounded by the two curves: x=100000(5*sqrt(y)-1) x=100000(\frac{(5*sqrt(y)-1)}{(4*sqrt(y))}) i'm having a lot of trouble trying to find the lower and upper limit of the two functions. I tried setting the two functions together and solving for y, but i get 0. then trying to...

Few stupid questions about polar curves and stuff... Okay, here's the first dumb question. I have to find the tangent line where r=2-3sin(T) at the polar point (2,pi). To find the slope, you just take dy/dx, and I come up with 2/3. I know that part is right. T=theta (I know it's spelled...

Banked Curves involving friction Problem: A car is traveling in a circle of a radius of 50 meters, on the surface the coefcient of static friction between the car's tires and the road is .3. With a banking angle of 30 degrees. (I attached a diagram) So here's what's known: Radius: R=50 m...

Hi, I was wondering how would I graph a sketch of these curves without knowing any values of them? They are orthogonal trajectories btw i) x^2 + y^2 = ax x^2 + y^2 = by ii) y = ax^3 x^2 + 3y^2 = b Thanks in advnace.

Space Curves --> Unit Tangent Vector and Curvature Here is the original question: Consider the space curve r(t) = (e^t)*cos(t)i + (e^t)*sin(t)j + k. Find the unit tangent vector T(0) and the curvature of r(t) at the point (0,e^(pi/2),1). I believe I have found the unit tangent vector...

Here is the problem: Determine the orthogonal trajectories of the given family of curves. y = \sqrt{2\ln{|x|}+C} This is what I've done so far: y = (2\ln{|x|}+C)^\frac{-1}{2} y' = -1/2(2\ln{|x|+C)(2/x) Now I understand to find the orthogonal lines I need to divide -1 by...

If it's energy, a photon must curve space. If it's rest mass a photon doesn't curve space and an object going at speed 0.99c doesn't curve space more than when it's not moving. A friend of mine asked me this question after asking two of his profs at McGill University and getting two...

Not sure if it's called "curves" in English, but what I am referring to is graphs that repeat over a given time. ie f(x) = sin(x) The problem I am having is understanding the following: Given: f(x) = sin(x) g(x) = cos(x) Find f(x) - g(x) by A(cos(x - x0)). Which gives: A(cos(x -...

Ok, bear in mind that I am DUMB when it comes to math... There, I said it... :cry: Ok, I was thinking about calculus and part of calculus is studying curves, identifying degree of curves, writing equations for curves, and stuff like that. Well it is simple to me to relate everything...

I have a question about reparameterizing curves. My specific question is "Reparameterize the curve with respect to the arc length measured from the point where t=0 in the direction of increasing t. r(t)=e^t*sint i +e^t*cost j" I understand the whole process about finding the answer, but I...

Thus far my professor showed us 3 ways to compute line integrals: Direct Potential (If curl F = 0) Homotopy Homotopic curve--- finding a curve q(t) that changes the path of integration, so that the L.I. can be computer much easier. My question MUST curl of any ForceField always have...

Hello all, I seem to be misunderstanding a concept; perhaps someone could point me in the right direction. My knowledge of physics is very basic so please have some sympathy. Thanks General relativity shows that gravity is caused by the presence of matter that curves space-time. But now I...

Does GR say that the expansion of the universe must exist? Would this mean that there is a tendency to flatten out the curvature of space? Would this imply that massive objects attract each other in an attempt to flatten out the space between them? Does higher curvature represent a...

Find the length of the parametrized curve given by x(t)=0t3+9t2+36t y(t)=-1t3-6t2+15t for t between 0 and 1. ok...thats the question. I have tried using the formula L = integral of (dx/dt)2 + (dy/dt)2 all square rooted but I am not gettin the rite answer...i have a bunch of these...

Can anyone show me websites or links that talk about lines, curves, functions and limits? It will be better if these sites or links are interactive. If not interactive, it's ok.

When you are trying to find an integral and you are dealing with two curves, and the formula calls for f(x) , I know that you do f(x) - g(x) [/tex] and put in that value for the f(x) in the original formula. When the formula calls for f^2 (x) , do you do (f^2 (x) - g^2 (x)) or [itex]...

This is the problem: find the area of the region bounded by the curves f(x) = x^2 + 2 and g(x) = 4 - x^2 on the interval [-2,2] I did the whole integral from -2 to 2 with (4-x^2) - (x^2 + 2) dx because the graph of g(x) is on top between the region bounded. But from my drawing, the points...

Find the area bounded by the y-axis and the curve x = y^2 - y^3 What exactly does the graph of x = y^2 - y^3 look like? And how do you set up the integration?

I need to find the area between y=x and y=x^2 So this is what I did: A = \int (x^2-x) \,dx Then I found the limits of integration x=0 and x=1 because that's where the two graphs intersect A = \int^1_0 (x^2-x) \,dx I ended up with an answer of -1/6 What did I do wrong?