Curves Definition and 778 Threads

Homework Statement Sketch the family of curves given and calculate and draw the envelope should it exist. Homework Equations X(t,Lambda) = r(cos(t),sin(t))T + (acos(Lambda),bsin(Lambda))T The Attempt at a Solution using the determinant of the partial derivatives wrt to t and...

Homework Statement At time t, a comet has the position R = (t2-1)i + 2tj At t = 2, find the radial and circumferential components of velocity and acceleration Homework Equations Vr = V * Ur Vθ = V * Uθ ar = a * Ur aθ = a * Uθ Ur = cosθ i + sinθ j Uθ = -sinθ i + cosθ j...

I'd like to have someone explain to me the purpose of the variable change in the proof of the following theorem: A parametrized curve has a unit-speed reparametrization if and only if it is regular. Proof: Suppose first that a parametrized curve γ: (a,b) → R^n has a unit-speed...

Homework Statement find the area bounded by : 4x+y^2=12 x=y Homework EquationsThe Attempt at a Solution f(x)= √4x-12 g(X)= x √4x-12=x √3x-12=0I'm lost how am i supposed to set them equal to each other if the second equation is y=x? can anybody help me please

Homework Statement find the area bounded by: y=X^2-2x y=X+4 Homework Equations HERE'S A LINK TO THE PROBLE: http://picasaweb.google.com/luaykhouri/UntitledAlbum# <embed type="application/x-shockwave-flash" src="http://picasaweb.google.com/s/c/bin/slideshow.swf" width="288" height="192"...

A curve in space is specied by the one parameter set of vectors x(t). Also given is a surface in space parameterised by x(u, v): x(t)= <2+t, -t, 1+3t2> x(u,v)=(u2 - v + u, u+5, v-2> A) Show that the curve intersects the surface in exactly two points. Show that xi = <4 - \frac{\sqrt{46}}{2}...

Homework Statement Find the area of the indicated region. Enclosed by y = e^x, y = 2, and the y-axis The Attempt at a Solution So I the area should be integral of e^x - 2 which = e^x - 2x . I'm not sure what to do with the y-axis it mentions?

Hi All, I have been battling with this question for a while. Given a conservative vector field, we know that there are infinitely many closed paths where the line integral evaluated is zero. In fact this is the requirement for a conservative vector field: Every line integral of any closed...

I looked in my james stewart book and didn't find any thing helpful about that and google didn't give me any useful results so is it possible and how to?

Homework Statement Hi all, I am trying to plot multiple curves in matlab. If i have the function: y=x^i where i goes from 1 to 10. I want to plot the function y for each i. Homework Equations The Attempt at a Solution x=[1 2 3 4 5 6 7 8 9 10] for i =1:10 y = x.^i end...

Find the area bound between y2 = x + 5, and y2= 3 - x.I can't figure out how to put limits of integration, the integrand, or really anything besides just the integral sign to work with Latex, so bear with me (or better yet, direct me to a tutorial! I will search for one after this post, if there...

these are fairly simple questions that only require you to plot points and then find a Cartesian equation of the curve. My question is when trying to solve for the Cartesian Equation, whether to solve for X first or Y? I will give an example. X=3t-5 , y=2t + 1 Graphing this is simple...

my question might be simple but my professor didn't really explain this.. how do you know what function to subtract from what to find the area between the two graphs.. i know you use integrals of f(b)-g(a) and f(b) is the function that is above g(a) but how do you find it out for complex...

Hi everyone. I came across this site yesterday during some targeted Googling and thought I'd give it a shot. I have a basic question about speed/torque curves for brushless DC motors. I would like to compute a speed/torque curve for a small three-phase brushless DC motor that I have. It...

Hi all. I'm wandering about the existence of closed asymptotic curves (curves having zero normal curvature everywhere) on minimal surfaces. I believe that the only minimal surface that admits closed asymptotic curves is the plane, but I cannot find a simple way to prove it. Here is where my...

Homework Statement A wire lies along the piecewise linear curve extending from the point (4,3) to the point (6,15) to the point (12,15). If the density of the wire is given by (xy)=3xy+2y, use a line integral to find the mass of the wire. Homework Equations The Attempt at a Solution...

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

1. Let R be the region bounded by the curves y = x2 and y = x + 2. (a) Sketch the region R and label the points of intersection between the two curves. (b) Suppose we rotate R about the x-axis. Compute the volume of the resulting solid. (c) What is the volume of the solid obtained by rotating...

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

Homework Statement f(x,y)=y-x i) compute the gradient ii) at the given point (2,1) compute the gradient vector gradf(2,1) iii) compute the level curve that passes through the point (2,1) iiii) on the xy-plane, sketch the level curve from iii and the gradient vector gradf(2,1) you found in...

we represent electromagnetic waves by sinosoidal curves. magnitude of what changes sinosoidally? or what does that represent?

Please guys i have only one shot and I tried but i couldn't her is the prblem http://img87.imageshack.us/img87/5229/27745883.jpg My Try: [PLAIN][PLAIN]http://img806.imageshack.us/img806/9801/scan0002y.jpg

Homework Statement two particles travel along the space curves r1(t)=<t, t2, t3> r2=<1+2t, 1+6t, 1+14t> Do the particles collide? Do their paths intersect? [b]2. Homework Equations if vector r(t)=<f(t), g(t), h(t)>, then lim r(t) t-->a = <lim f(t)t-->a, lim g(t)t-->a, lim h(t)t-->a>...

Homework Statement Using the domain 0 < x < pi sketch the two functions y=2sin(x/3) and y = 2x/pi on the same axes. Find the area Homework Equations The Attempt at a Solution I have sketch the graphs. And attached my working so far - can someone confirm my workings so far...

Homework Statement Find the area of the lemniscate r2=6cos(2w) located to the right of the line r=3/2sec(w). Homework Equations Area of a polar region is the integral from a to b (in this case a and b are where the curve intersects the line, I believe) of 1/2*r2d(w). The Attempt at...

Homework Statement Then find the area S of the region. (between the curves) Homework Equations A = \int_a^b f(x)-g(x) dxThe Attempt at a Solution First I plotted both equations, determined the top and the bottom functions and found where they intersected (calculator). Then I set up the...

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Homework Equations \int_a^b [f(x) - g(x)]dx The Attempt at a Solution f(x) = 6x-x^2 g(x) = x^2 a = 0, b = 3 \int_a^b [f(x) - g(x)]dx \int_0^3...

Homework Statement (a) Find the area A, as a function of j, of the region in the 1st quadrant enclosed by the y-axis and the graphs of y = x ^ (1/3) and y = j for j > 0. (b) What is the value of A when k = 2 (c) If the line y = k is moving upward at the rate of 1/2 units per second...

This particular problem is just confusing me in the setup. I need to find the area that is inside both: r=sqrt(3)cos(theta) and r=sin(theta) It makes a petal type shape. I was beating my head around for a while, but I reasoned that since the equation used to find the area cuts out in a straight...

[b]1. Find the area between the curves y=4xe^-x^2, y=abs(x) [b]2. intersection points are 0 and sqrt(-ln(1/4)) [b]3. help!

Homework Statement Find the shortest distance between, y = x^{2} - 8x + 15 and, 2y + 7 + 2x^{2} = 0 Homework Equations The Attempt at a Solution Rearranging the 2nd function into a function of y in terms of x, y = -x^{2} - \frac{7}{2} From here I was able to graph...

Hi There, I have been working on fluorescence decays of the fluorophores whose lifetimes are comparable to the instrument response function(IRF) of my device. The technique I use is based on Time-correlated single photon Counting(TCSPC). I have been fitting the decay curves using...

Homework Statement Basically I have two problems that are asking for the partial derivative with respect to x and y at a certain point on a level curve graph, and a contour map. How do you go about doing these? There is no function given, so I don't really know what they expect you to do...

First, let me start by apologizing for the length of this post. i do in fact have a question about a problem that i couldn't solve (at least not the way i wanted to solve it), but first there is a fair amount of foreground information i must lay down...beyond this foreground information, this...

Does anyone remember a program (or know of something similar!) which, given a compilation of data, would search for equations which best fit the data? The one I'm thinking of came out ~ a year ago. It was a Windows-only program but it worked fine under wine. Unfortunately my time spent on...

Ola, If we have two curves, and they cut them selves in a way like these two: y=x^2 and x^2+(y-1)^2=1. Does it always mean that those two curves in a cut point would have a same tangent, in other words do they need to have the same derivative in that spot? Thanks!

Homework Statement One mole of a dilute gas initially has a pressure equal to 1.00 atm, and a volume equal to 14.0 L. As the gas is slowly heated, the plot of its state on a PV diagram moves in a straight line to the final state. The gas now has a pressure equal to 2.00 atm, and a volume...

Dear all, I am currently doing my research deal with the Jacobian, Arithmetic and Pairings of the hyperelliptic curves ( for pure mathematics). I still at the stage of literature review. To enable me study the hyperelliptic curve, I will start with the elliptic curve and I need to read the...

Homework Statement Calculate the area between the curves y = sin 2x and y = cos x from x = to x = 90 degrees Homework Equations Using the difference function: ∫(upper = 90) (lower = 0) [sin2x - cos x] The Attempt at a Solution (sin 2x) - (cos x) = ∫ sin 2x - cos x = ∫-0.5...

Express the following in cartesian curves in polar form i) 4x-5y=2 Not sure how to do this ii) (x-3)^2+(y-4)^2=25 r=9cos16(theta) Is this correct ? Any help would be great

For the following curves i) y=x^2+4x-1 ii) y=-2+or-Square root(x+5) a) Sketch both the curves on the same sheet of graph paper- against the same axis I have done this, although I have not shown it here b) Determine with proof, whether the above curves are related. Not sure how to do this...

Find the area of the region in the plane enclosed by the cardioid r = 4+4\sin{\theta} The book explains that "Because r sweeps out the region as {\theta} goes from 0 to 2{\pi}, these are our limits of integration."

I am having trouble with this question: (QUESTION AS ATTACHED) This is what I tried to do: I found the intercepts of the difference of the two functions which I found to be only 8. Then I integrated this into the new function: \int{\sqrt{2x}-x+4}. with limits of 0 and 8 (I don't know...

Homework Statement I have to find some level curves for: f(x,y)=1-|x|-|y| The Attempt at a Solution So, if we call S at the surface given by the equation z=f(x,y), then z=1\Rightarrow{-|x|-|y|=0}\Rightarrow{x=y=0} \therefore P(0,0,1)\in{S} Now, that particular case its simple...

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=5 sqrt(x), y=3 and 2y+4x=9 Homework Equations Integral of right function - left function if integrating with respect to y F(b)-F(a) The...

I am looking for math software that will fit a set of points with a cubic spline (or other technique)...then allow the user to change the shape of the curve by dragging it...and continuously fit the curve as the dragging is occurring (or fit the curve after the dragging has stopped). The point...

Homework Statement Find the set of values of m such that the asymtote of the curve, y=\frac{3(m+1)x+m-2}{(m-2)x+3m} intersect at a point above the line y=3x-2 Homework Equations The Attempt at a Solution Vertical asymtote, x=-3m/(m-2) horizontal asymtote, y=3(m+1)/(m-2)...

These definitions seem to suggest that the same subset of M could be the range/image/arc of many different curves, each having a different parameter. Is that right, or should I think of a curve as an equivalence class of such maps?

Homework Statement See figure. Homework Equations N/A The Attempt at a Solution I've dealt with parametric equations for lines before in my linear algebra class but I'm not sure how I'm suppose to model two curves with one. Anyone have any suggestions?

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region Homework Equations The Attempt at a Solution I got a...