Tangent Definition and 1000 Threads

Homework Statement Determine the coordinates of the points on the graph of f(x) = \sqrt {2x+1} where the tangent line is perpendicular to the line 3x+y+4 = 0 Homework Equations f(x) = \sqrt {2x+1} 3x+y+4 = 0 The Attempt at a Solution For this, I was going to find the...

Hi there, Is there an "easy" way to find a tangent space at a specific point to an implicitly defined manifold? I am thinking of a manifold defined by all points x in R^k satisfying f(x) = c for some c in R^m. Sometimes I can find an explicit parametrization and compute the Jacobian matrix...

Homework Statement Find parametric equations for the tangent line at the point (\cos(\frac{4 \pi}{6}) ,\sin(\frac{4 \pi}{6}) ,\frac{4 \pi}{6}) ) on the curve x=\cos t,\ y=\sin t, \ z=t Homework Equations The Attempt at a Solution Took the derivative r'(t)=( -sint...

Homework Statement Find the unit tangent vector T(t) to the curve r(t) at the point with the given value of the parameter, t. r(t)=<e^(2t), t^(-2), 1/(3t)> t=1 Homework Equations none The Attempt at a Solution So first I took the derevative to get r'(t) which I got to be...

Kind of an odd question, but here goes: can anyone offer any examples of physical systems that include the use of the hyperbolic tangent function in their mathematical solution?

Homework Statement I've never seen such a problem before: Find the two straight lines that are perpendicular to y=0.25x and tanget to the curve f(x)=1/xHomework Equations y=0.25x ; f(x)=1/x The Attempt at a Solution Using the power rule, I found the derivatives of: f(x)=-x^{-2} and y=0.25...

Homework Statement limit as x->\infty of arctan[(1/x)-1] 2. The attempt at a solution Well, my graphing calculator is showing a vertical asymptote at x=0 and a horizontal one at x=(what I think is) -\pi/4 I'm not really sure how to solve this though... hence me being here : / EDIT...

Tangent function vector? Homework Statement i know the formula for this problem. My homework was to like 5 of these and got the other 4. now stuck on the algebra part. please take a look and let me know where to go from here. problem is consider the vector function given below: r(t) =...

Homework Statement Find the tangent plane to the surface x2 + 2y2 + 3z2 = 21, which is parallel to the plane x+4y+6z=0 Homework Equations Gradients. The Attempt at a Solution Here is my solution: So gradient of the surface is (2x, 4y, 6z). The normal of the given plane is (1,4,6)...

Homework Statement If f(x)= 3x^(2) - x + 4, find the values of m for which line y=mx+1 is a tangent to the graph of f?Homework Equations NoneThe Attempt at a Solution Well first you have to get the derivative of the function which is 6x-1...Then what? There are no points given...I tried...

I am working through a book on Kahler manifolds and for one of the proofs it states that the maximum exterior power of TM is m (where M has complex dimension). Could you explain why this is the case rather than the maximum exterior power being 2m.

Homework Statement I must evaluate the indefinite integral: \int x \arctan{x} dx Homework Equations I am using the following format to perform the integration: \int u dv = uv - \int v du The Attempt at a Solution I have tried working the problem substituting x in for u and arctan...

Hey I'm trying to understand how we arrive at the formula for the tangent plane to a surface. An image of what I'm talking about it shown below. I think understand all the parts up to part c, but i don't see how we arrive at that final formula. The image of first part of the solution is...

So I'm looking at this example in my textbook where they're trying to find the vert. & horizontal tangent lines of r = sin Θ, 0 < Θ < pi. they say to first change it to parametric equations where x = r cos Θ = sin Θ cos Θ and y = r sin Θ = sin Θ sin Θ = sin^2 Θ But now I'm just really...

Homework Statement Find the two points on the curve y=x^4-2x^2-x that have a common tangent line.Homework Equations See below.The Attempt at a Solution y=f(x)=x^4-2x^2-x \frac{d}{dx}\right((x^4-2x^2-x)=4x^3-4x-1 To my understanding, two points A,B who have a common Tangent such that T_A=T_B...

I'm taking calculus online and I need help figuring out how to solve the following problem. My book and notes given from my teacher do not show how to solve problems like this and I keep ending up with answers that don't work. The question is; Find f '(a) when f(t)=(3t+3)/(t+6)...

Given present theory, how would a laser photon stream behave at a tangent point to an event horizon (EH)? Is it possible for a photon stream to orbit a black hole? Could the beam be split at the EH with one branch spiraling into the black hole while one branch follows some geodesic (perhaps not...

Homework Statement I've been working on this problem for several hours with no luck. Any help would be appreciated. (It's not homework) A thin rod of mass M and length L is hinged at the bottom, and almost balanced vertically. It starts to fall. Find the tangential component of the force...

Homework Statement Find the equation for the tangent line to the curve f(x) = 2x3 - 5x - 3 at x = 2 Homework Equations How do i start this? I'm really confused and have an assignment with a bunch of these questions due tomorrow by midnight... if someone could help me that would be...

Find the equation of the line tangent to the graph of y=x^2 at the point (1/2,1/4) and how to find that?

Homework Statement I am given a one form Psi = zdx -xydy and two vectors v(1,1,-2) and w(-2,1,1) both tangent vectors of R3 at point P(2,-1,0). I am asked to find dPsi(v,w). Homework Equations Lie bracket? The Attempt at a Solution I know how to computer Psi(v) at p but this...

I've encountered a definition of the tangent vector via the notion of derivations on the manifold and I have some problems with it. I would actually like to show that every derivation can be expressed as a directional derivative, but I'm not ver successful in doing so. I have this definition...

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ) y = sec(θ) (1 , √2) y = ? attempt ; y - y1 = m(x-x1) y = √2 x = 1 y1 = sec(θ) x1 = tan(θ) substituting and solving it...

okay i came up with doing the gradient of the ellipsoid. Then set that equal to the vector, <4,-4,6>. I solved and got x,y,z = 1,-2,1 I looked at the answer key and it said (1/3) (1,-2,1) Does anyone know where the 1/3 came from?

In Euclidean vector spaces the derivative of the position vector of a running point of a curve is the tangent vector of the curve. In thehttp://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf" , on page 78 appears a vector which can be regarded as position vector in a Riemann space...

Homework Statement Let f(x)=a(7-x^2) find in terms of a, the equations of the lines tangent to these curves at x=-1. Homework Equations ? The Attempt at a Solution So I took the derivative of f(x). f'(x)=a(-2x)+7-x^2 then i plugged in -1 into f'(x) and i got f'(-1)=2ax+7+1=2ax+8...

Question is in the title. Seems a lot of people throw that statement around as if its obvious, but it isn't obvious to me. I can kind of see how it might be true. If you take a group element, differentiate it wrt the group parameters to pull down the generators, and then evaluate this...

Homework Statement I have a homework that i couldn't do :( can you explain it to me please ? the problem is : find all values of x=c so that the tangent line to the graph of f(x) af (c , f(c)) will be horizontal http://img13.imageshack.us/img13/4222/scan0002izs.jpg The Attempt...

Homework Statement What is the slope of the line tangent to the polar curve r=2theta at the point theta= pie/2 Homework Equations r = xcos theta r= ysin theta The Attempt at a Solution I kept getting zero but the answer is -2/pie. Can anyone give me a hint? :) Thanks!

In trying to understand why not all tangent bundles are trivial, I've attempted to prove that they are all trivial and see where things go wrong. Unfortunately, I finished the proof and cannot find my mistake. Here it is: Let M be an n-manifold with coordinate charts (U_\alpha...

Homework Statement [/b] My book talks about find the two tangent lines at the point (0,2) for http://mathbin.net/equations/7402_0.png and http://mathbin.net/equations/7402_1.png .[/URL] It says that t then is equal to pi/2 and -pi/2. I do not know how to they solved for this t. Any help?

So, I just learned in class that to get inverse cot-1(x) I have to do tan-1(1/x). Then add either pi, or 180 depending on wheather we are using radians or degrees. And I don't understand this. If x is cot, then when we do 1/x, shouldn't we get tan? And after than isn't it enough to just do...

Homework Statement Tangent plane goes through point P=(a,b,f(a,b)). Any point on the plane is then Q=(x,y,z)=(x,y,f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)) (fx and fy are partial derivatives) and the vector \overline{PQ} is on tangent plane. Calculate dot product n.\overline{PQ} and show...

Homework Statement Find the equation of the tangent line on the function, f(x) = X^{2}-4x+1, which is perpendicular to the line, x+2y=10. Homework Equations The Attempt at a Solution x+2y=10 2y = 10-x y=-1/2x+5 Slope of perpendicular is -1/2, so slope of tangent is 2. The...

Homework Statement r(t) = sin t (i) + cos t (j) + t k Find the equation of the line tangent to r(t) at the point (0,1,0) If you plug in 0 into to for r(t), you get (0,1,0). Thus t must equal o. To find the vector of r' (t) or the derivative of r(t) this equals = < cos t, -...

Find the equation for the line that is tangent to the given formula if y = pi/2 when x = 0 Homework Equations (x+1)dy - [(1/2)secycscy]dx = 0 The Attempt at a Solution I tried to do this, and I got that dy/dx = 1 / (0*0), which is infinity. So... y = \infty?

Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5

Determine the equation 1 the tangent to the given function, at the given point. y = (3x^-2 - 2x^3) , @ (1,1)

The line y = 8x + b is tangent to the curve y = 2x^2. Determine the point of tangency and the value of "b"

My teacher wrote an alternative equation on the board for curvature, and I am wondering how it is true: k = | dT/dt / |dR/dt| | where T is the unit tangent vector. I know k = |R' x R''| / |R'|^3 = |dT/ds| but I am not sure about the formula in question. How is it true/derived?

Homework Statement find the slope of the tangent line whose g(x)=x^2-4 at point (1,-3) Homework Equations lim f(x+Δχ) -F(c)/ (Δχ) The Attempt at a Solution g(x)= x^2-4 G(1+Δχ)= (1+Δχ)^2-4 ==> Δχ^2+2Δχ-3 lim (Δχ^2+2Δχ-3) - (-3)/(Δχ) = 0 but in the book the answer is 2 so what...

Hi everyone, I'm an 18-year-old from Germany and I'm making use of MIT's OpenCourseWare programme. Currently, I'm watching the Calculus II course, and am having some trouble understanding how to find the equation: z=z0 + a(x-x0) + b(y-y0) by using parametric equations/vectors. a and b being...

Homework Statement i can't solve it! im really lost. i know you find f''(x) (i got 9e^3x +12) but i don't know where to go from there what would i do on my calculator?

Homework Statement A) Find all points on the graph of f(x)=x^2 with tangent lines passing through the point (5,0). B) Show that no line tangent to g(x)=1/x passes through the origin. These are problems from a lab problem solving assignment. Homework Equations y=mx+b f`(x) =...

Homework Statement Find the equation of the tangent plane at (2,3,2) to the surface below. x^2 + y^2 - xyz = 1 The question asks me to do this in two way, one is to view the surface as the graph of a function of two variables z = g(x,y). and the other one is to view the surface as a...

[b]1. Here's a theorem about the tangent function. tan(x) = c iff 1: x = tan^-1*c or 2: x = tan^-1*c+n(180) for some integer n. Find a solution to tan x = 1 between 270 and 450 degrees. [b]2. [b]3. I am not really sure how to go about starting this problem. I have only two...

Homework Statement My professor gave us 4 points A(2,3,-5) B(-2,5,1) C(9,0,4) D(3,-5,8) So I must find an equation of the sphere that is tangent to 2 planes. These 2 planes are 18x + 39y - z= 158 18 x + 39y -z = -149 Homework Equations equation of sphere C(h,k,l) (x-h)^2 + (y-k)^2...

3.) Give the equation of the line tangent to the curve at the given point. a.) (y)(tan^-1 x) = x*y at (sqrt(3),0) b.) ln y = x^2 +(2)*e^x at (0, e^2) Please help me with this problem, I am stuck. Here is some of my work process: i have no idea how to solve for y in...

Homework Statement I seem to remember that a parameterized a(t) curve in \mathbb{R}^3 that one can construct the tangent from the slope of a'(t) and the curve itself. such that the tangent line L = a(t) + s * a'(t) to a. This is supposedly a straight line in \mathbb{R}^3. To make a...

Homework Statement If the tangent line to y = f (x) at (9,7) passes through the point (0,6), find the following. (a) f (9) (b) f ' (9) Homework Equations f '(x) = f(x+h) - f(x)/h ? The Attempt at a Solution I really have no idea how to even begin going about this one, so a...