Curves Definition and 778 Threads

I learned that vertifcal tangents occur at a parametric curve if the derivative of the curve is undefined. That is given dy/dx = dy/dt / dx/dt, a vertical tangent occurs when dx/dt = 0. I don't understand why this is so. I know that vertical tangents occur when the slope is infinite, but...

Show that for all values of t, the point P with the equation x=2t^2, y=t^3 lies on the curve 8y^2=x^3 Find the equation of the tangent to the curve at point P. The tangent meets the curve once again at point Q. Find the coordinates of point Q. I can find the equation of the tangent. After...

Homework Statement Find the area of the region enclosed by the following curves: f(y)=1-y^2 g(y)=y^2-1 Homework Equations The Attempt at a Solution I'm confused by the graph because the region enclosed has positive and negative parts, and I can't determine whether f(y)>g(y), g(y)>f(y), or...

We were given a graded assigment and one of the question asks. Prove that all curves in the family y1=-.5x^2 + k (k any constant) are perpendicular to all curves in the family y2=lnx+ c (c any constant) at their points of intersection. I found the derivatives of y1 and y2 and they are...

Okay... so here's the problem I'm working on. Suppose you're observing a celestial body in space that is following a (relatively small) elliptical orbit around a larger distant celestial body (let's say it's at a distance d such that d>>a, where a is the semi-major axis of the orbit). For...

I just finished learning the fundamental theorem of curves in 3 dimensions. As a reminder, this is the theorem that states that a continuous, C infinity, unit speed curve in 3d is uniquely determined by its curvature and torsion (up to actions by SE(3), that is rotations and translations)...

I am trouble with problems that don't list each function f(x) or g(x). The book sets them equal to y. Every time I do these I'm getting them wrong. When I check the solution, I'm mistaking f(x) for g(x) or vise versa. So is there a way to tell which y is f(x) or g(x)?

A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.84. at what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction...

I have three points on a Y= -ax^2 + bx + c graph (negative parabola). I don't know how to find the equation with this information. Tangent lines? Help.

A thought occurs... In a world devoid of curved lines, can we create a circle using only straight rigid lines? If we take a square as our starting block, then use 4 straight lines to cut off its 4 corners at 45 degree angles, we now have a perfect octagon. If we now take 8 straight lines...

Hello, are all Oval Shaped Cartesian Curves" +/-(x^2) " or we can have it with other degrees??

Hi, I am having a little trouble with this one, how do you do them when no boundaries are given? y=sin \frac{\pi x}{2} and y=x how do i find the boundaries?

How would one go about finding an analytical solution to the following ODE note that we are trying to find y(x) subject to... (x*y'')^2 - (1 + (y')^2) = 0

Hi all, I'm having a problem with this subject and I was wondering if anyone could confirm/comment on my understanding. As I understand it, in a typical transformer, an AC current is supplied to a primary coil which induces an oscillating flux within the core. If the core is made of a...

I need to find the area that's inside both of the following curves: r = \sin\theta r = \cos\theta I know that I should have to subtract the area of the one curve from the other and I know the area formula for polar coordinates, but I just can't see how to set this one up any help or...

Find the area of a figure bounded by the equilateral hyperbola xy = a^2, the x-axis, and the lines x = a, b = 2a. My work: The equations of the lines and curves involved here are: xy = a^2 y = 0 x = a I don't know how b=2a is treated as an equation of a line here & hence I am puzzled as how to...

Hi Could someone please give me an idea on how to go about this problem Find the volume of the curve genereated by revolving the area between the curve y =(cos x)/x and the x-axis in the interval pie/6 to pie/2 Thanks a lot..

Write, but do not evaluate the integral that will give the area between y = cos x and y = x/2 - 1 , bounded on the left by the y-axis I've sketched the graphs, so I know that y = cos x is above y = x/2 - 1 , so the indefinite integral to solve would be \int (cos x) - (x/2 -1) dx I...

Good morning to all. By laboral reasons I am reading about digital signatures and "public key" cryptography. The most popular of the cryptographic methods related to digital signatures (RSA) is only an application of the "little Fermat theorem". This theorem belongs to "baby" number theory...

In a cooling curve of a single substance there is a thermal arrest point where the liquid turns into solid. My laboratory manual mentions that in a cooling curve containing two liquids (A + B), in addition to the arrest there is a second point called a "break". It says the point at which solid A...

"The temperature of space is given by \phi (x,y,z) = xy + xz . A fly is flying in space and at each point (x,y,z) of its journey it flies in the direction \mathbf{F} (x,y,z) in which the rate of increase of temperature is maximum. (a.) Calculate F(x,y,z). (b.) Find the curve along which the fly...

Hello, thank you for helping. My Question: On a banked race track, the smallest circular path on which cars can move has a radius r1 = 107 m, while the largest has a radius r2 = 163. The height of the outer wall is 18 m. Find the smallest speed and largest speed at which cars can move on...

I have been asked to find the area between the following curves f(x)= x^3 -9x^2 +18x and g(x)= (-x)^3 +9x^2 -18x I started out by finding the points of intersection, which I found to be 0, 3, and 6. I then integrated |f(x)-g(x)|and evaluated between 6 and 0. I got an answer of zero but it...

I'm stuck on this problem. I am hoping someone can walk me through it or get me past my choking point. The problem states: Two equations have two shared tangent lines between them. Find the equations of these tangent lines analytically. g(x)=x^2 f(x)=-x^2+6x-5 The first step I took was to...

hi! Thanks for the advice, I managed to find the intersection points, but I seem to have run into a problem. I set up the integral as follows: (4-x^2) (for 1 to 2) + (4 - 1/x) (for 1/4 to 1) this worked out to ((8-8/3) - (4 - 1/3)) + (4 - (1 - ln1/4)) (16/3 - 11/3) + (3 + ln1/4) 5/3 +...

hi, the question goes as follows: y = x^2, y=1/x, y=4 for the first quadrant. This may be a dumb question :blushing: but how do I figure out the points at which these three intersect? Do I first set the first two equal to each other and then set the resulting equation equal to 4? Thanks...

I have this problem bothering me. I am asked to find the volume bounded by two curves, when they were rotated about the y axis. I did it as usual. Functions are y1 = cosx +1 [tex] y_2 = 2(\frac{x - \pi}{\pi}) ^2[/itex] The way I did the problem is to find the volume of revolution of...

I know how to do this graphically, but I can't remember how to set it up the long way. The equations are: y^2=x and y=x-2 I know it should be easy, but it's late and I can't think...

Hi. I'm new here. :) I was wondering if anyone could help me out with this problem... i'm supposed to find the region bounded by: y=x+1 y=e^-x x=1 i think i should find the other point of intersection but i forgot to do that (i haven't taken a math course for about 4 years). please help!

A curve of radius 170 m is banked at an angle of 22°. At what speed can it be negotiated under icy conditions where friction is negligible? Can someone explain how to get the answer for this question? Thanks

1. I am given a curve defined parametrically by x= 2/t , y=1-2t i have found the equation of tangent at t=-2 to be y=4x+9, they have asked whether it cuts the curve again. how do i find that, since i don't know the original equation of the curve and can't solve them simultaneously. 2. Also...

Hi, I'm having trouble drawing the level curves of a function because I can't really visualise what's going on. f\left( {x,y} \right) = \frac{{2xy}}{{x^2 + y^2 }} In polar coordinates (x,y) = (rcos(phi),rsin(phi)) I get:f\left( {r\cos \phi ,r\sin \phi } \right) = \sin \left( {2\phi }...

What other curves are there that cannot be described by the above? Are trigonometric functions actually a special case of exponentials with complex powers?

Titration Curves - Help needed I really need some help in this, I don't understand how to make a titration curve. I have 50ml of a 0.1 M solution of formic acid with a 0.1 M solution of NaOH. I know that the pKa of the formic acid is 3.74 but i don't know how to get the pH or H+. I've hit a...

Find an equation of the tangent line to the curve with parametric equations x=tsint, y=tcost at the point (0,-π). went dy/dt / dx/dt --> cost - tsint/sint + tcost t not given so figured it could be: x=t(sin(1)) --> t= x/sin(1) or y=t(cos(1)) --> t= y/cos(1) wondering if...

Could anyone explain to me how to go about solving these problems? Example: A Car is driven around a circe with a radius of 200m, bank angle 10 degrees. The static frictional coefficient is 0.60. Calculate the maximum velocity the car can travel (Vmax). Please help! I did this, but am not...

I know there are some, but I can't think of any examples. I asked my teacher after class but she couldn't think of any either.

I am trying to find and graph the level curve f(x,y)=\sqrt{x^2-1} that passes throught the point (0,1), as well as its domain and range. I am not sure if my reasoning is right, so let me know if I got the wrong idea. For the graph I have x = 1 which is independent of y and is just a...

when three curves intersect,i mean like the intersection of three straight lines to give a triangle,how can one find the area between the curves

This time the news is that on 21 September this paper was accepted for publication in Astrophysical Journal. It will appear in January. http://www.arxiv.org/abs/astro-ph/0506370 Galaxy Rotation Curves Without Non-Baryonic Dark Matter J. R. Brownstein, J. W. Moffat 43 pages, 7 figures, 4...

If you wish to negotiate a curve while traveling at high speed, the largest radius should be followed through the curve in order to minimize the lateral forces acting on the car. However, in practice it doesn't really work this way. I have long noted that the car can actually be more stable...

Thanks on the help on the other thread. I, however, have yet another question. In the line integrals, how is it that we're integrating the various components to the limits of the curves, it seems like the curves really don't matter, just their limits. Can someone explain how the curves are...

Stewart uses the chain rule to show how to find the tangent to parametric curves. Given: x=f(t) and y=g(t), and that y can be written in terms of t, in other words, y=h(x) then the chain rule gives us, dy/dx = (dy/dt)/(dx/dt). Thats fine. The same argument holds for polar coordinates...

I am having trouble finding the area between 2 polar curves... I have the procedure down, but the bounds are throwing me off. Any help with understanding how to bound would be great appreciated! I have attatched one problem that I am having hard time with and the work I have done. I know...

I am having trouble finding the area between 2 polar curves... I have the procedure down, but the bounds are throwing me off. Any help with understanding how to bound would be great appreciated! I have attatched one problem that I am having hard time with and the work I have done. I know...

calc 2 problem (area bound by parametric eq.) I'm having a problem with this question: Find the area bounded by the curve x=cos{t}\ y= e^t, 0\geq t\leq\pi/2\ , and the lines y=1\ x=0 ... I came up with \int e^t(-sin{t})dt from 0\to\pi/2 But apparently I'm missing steps...

in case if might be of interest http://arxiv.org/abs/astro-ph/0506370 Galaxy Rotation Curves Without Non-Baryonic Dark Matter J. R. Brownstein, J. W. Moffat Submitted to ApJ, June 20, 2005. 43 pages, 7 figures, 4 tables, 101 galaxies "We apply the modified acceleration law obtained from...

well first off, here's the problem: A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.997. At what angle should the same curve be banked for the car to negotiate the curve safely at the same...

For a flat road, where a car is turning, the max speed can by found by: Fc = Ff mv^2/r = uFg = umg v = sqrt(rug) For a banked road with angle T, the max speed (i think i did this wrong) mv^2/r = Fnsin(T) + Ffcos(T) mv^2/r = mg*sin(T) + umg*cos(T) v = sqrt(rg(sin(T) + ucos(T)) but...

Hey guys, I am curious if I am setting this up right. Could you take a look and make sure I am on the right path? I have three questions. 1) I am trying to find the area bound by y=x^2 and y=4x+5 Upper function y=4x+5 Lower function y=x^2 For my integral I have \int^{5}_{-1}4x-5-x^2...