Curves Definition and 741 Threads

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...

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 My result gave me an...

Hello, given a parametric curve \mathbf{r}(s)=x(s)\mathbf{i} + y(s)\mathbf{j} + z(s)\mathbf{k}, my textbook says that tangent vector having unit-magnitude is given by \mathbf{r}(s)=x'(s)\mathbf{i} + y'(s)\mathbf{j} + z'(s)\mathbf{k} I don't understand the proof that it has unit magnitude...

Homework Statement Find the gradient of the function at the given point, then sketch the gradient together with the level curve that passes through the point. f(x,y) = y - x (2,1) Homework Equations gradient of f = (df/dx)i + (df/dy)j The Attempt at a Solution df/dx = -1...

Homework Statement "Find the area of the region which is inside the polar curve r=5cos(theta) and outside the curve r=4-3cos(theta)." Homework Equations The Attempt at a Solution I keep coming up with 18.708, but it says that's incorrect. I don't know what I'm doing wrong...

1. A roller coaster of mass 320 kg (including passengers) travels around a horizontal curve of radius 35 m. Its speed is 16 m/s. What is the magnitude and direction of the total force exerted on the car by the track? Homework Equations The Attempt at a Solution

Hello all. This is not homework, i stumbled upon it looking for information for my physics.. I have some background in calculus and am just wondering if anyone would have any idea on how you'd solve this area problem.. all i have is a picture of it and not any equations of the lines. Thanks.

dear all, Hello, I need your help in this matter, the discription of the subject is: we have two input vectors ( included in one vector): T ( temperature ) and H ( humidity ), there is a corresponding one output P ( power demand ), and all these data are normalized I...

Hello everyone, I am working on trying to model a bouncing light ray between two curves, and I would like to model it in Mathematica. However, I do not know what syntax or how to go about typing the code in. I tried to find examples on the Mathematica Documentation Centre but the examples...

Hi, I am currently using MATLAB to do some work on simple closed curves in the plane. In order to make this work quite general I have opted to use a matrix which stores (x,y) coordinates of points on my curve (rather than use a function). I want to feed some interesting curves into my code...

Hi guys, I was trying to sketch a polar curve but my curve was different from the curve on maple(I plotted the same curve on maple). Homework Statement Here is the whole question, I am using t as theta. The hyperbolic spiral is described by the equation rt=a whenever t>0,where a is a...

I need something that I can use to draw a few simple 2D images, that don't have to look pretty. I really mean "draw" (with the mouse) and not generate from a formula, and a minimum requirement is that the program can at least let me try to draw a smooth curve with the mouse and then smooth it...

Homework Statement let C1 : y = x - 1/2 x2 and C2 : x = y - 1/2 y2 be curves on the xy plane. 1. find the equation of the tangent to the curve C1 at x = k 2. suppose the line obtained in 1) is also tangent to the curve C2. find all values of k and the equations of the tangents. 3...

Elipse [0,2pi] x=acosT y=bsinT\ by symmetry 4I(y,x) chossing the limits of integration my text is showing 4I(y,x,0,a) T=0=>x=a T=pi/2=>x=0 so wouldn't this be 4I(y,x,a,0) proceeding inthe books case gives pi(ab) while in the later case gives -pi(ab) Also x= (t-1)/t y=(t+1)/t...

Lately I have been going nuts trying to find a definitive answer to this relatively simple question. Why does light curve around bodies of mass? After a bit of digging I have found 3 answers. 1. Light follows the curve of space-time. 2. The mass of a photon is attracted by gravity of the...

Homework Statement Find the area bounded by the curves given by the graphs x = 4 - y^2 and x = y^2 - 2y The Attempt at a Solution I don't know how I can integrate these curves as they are not functions. Can someone tell me to get started on this problem? Thank you

Homework Statement The problem asks to find the shortest distance between two points on Earth, assuming different equatorial and polar radii i.e. the coordinates are represented as: x = a*cos(theta)*sin(phi) y = a*sin(theta)*sin(phi) z = b*cos(phi) Homework Equations The Attempt at a...

Homework Statement So the curves are: y = \frac {x^{4}}{x^{2}+1} and y = \frac {1}{x^{2}+1} The Attempt at a Solution So first the limits of integration are: \frac{x^{4}}{x^{2}+1} = \frac{1}{x^{2}+1} (x^{2}+1)\frac{x^{4}}{x^{2}+1} = \frac{1}{x^{2}+1} (x^{2}+1)...

Homework Statement The curves are: f(x)= x^{2/3} and g(x)=x^{3/2} Homework Equations I am assuming that: x^{2/3} = x^{3/2} is going to give me the limits of integration but I don't know how to solve for x on this equation. Could also put it this way...

I've always admired the way Einstein approached gravity, -which had previously been treated as an a attraction, that is, a determined kinematics that had to be accounted for by a force-,from a completely different point of view, looking at it as the curvature that matter-energy produces in the...

Homework Statement find the Area Bounded by the two curves, y=|x+1|, y= - ( x+1)2 + 6 Homework Equations y=|x+1|, y= - ( x+1)2 + 6 The Attempt at a SolutionA= Integration of | f (x) - g(x) | x+1= f(x) -(x+1)2 + 6= g(x) getting the limit of integration: x+1= - (x+1)2 + 6 x2 + 3x - 4=0...

Homework Statement Let S be the solid region bounded by the paraboloid z = x^2 + y^2 - 4 for z \le 0 , 0 \le x \le \sqrt{4 - y^2} and 0 \le y \le 2 . Find the Cartesian equations of the curves if the surface S intersects the xy,xz , and yz planes. The Attempt at a Solution...

Hi there If possible can someone please review my understanding of this question. Homework Statement At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2 Homework Equations The Attempt at a Solution We are given the gradient of the...

Homework Statement I am working on a Calculus I project and the last question has me stunned. I would really appreciate some assistance in this. Maybe a push in the right direction. So here is the problem word for word. There is also an attachment containing a picture of the problem...

Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help. Thanks.

Homework Statement A particle of mass m = 3.0 kg moves along the x-axis through a region in which its potential energy U(x) varies as shown in the Figure. When the particle is at x = 8.5 m, its velocity is 2.273 m/s. http://i118.photobucket.com/albums/o...yfe42/phys.gif D.) What...