Tangent Definition and 1000 Threads

Homework Statement Now, I decided for no real reason to derive a formula for the hyperbolic tangent using only what I know about the derivative of the inverse hyperbolic tangent. However, what I have looks wrong, and I'd like to check it here. Homework Equations \frac{d...

Homework Statement For each function, find the equation of the tangent at the given point a) f(x)= 1/ squareroot(2x+1) at x=4 The Attempt at a Solution I'm fairly lost, I understand I'm looking for an equation of a tangent, but I don't understand where to begin, find the derivative...

it is quite peculiar i know you do not want to embed the manifold into a R^n Euclidean space but still it is too peculiar it is hard to develop some intuition

Homework Statement Here's a worked problem, I can't understand how they have evaluated T at the given point (in part c): [PLAIN]http://img31.imageshack.us/img31/3725/97856984.gif The Attempt at a Solution I just substituted (0,1, \pi/2) into r'(s) but \frac{1}{\sqrt{2}} cos...

can anybody tell me why electric field of lines are tangent to direction of electric force please be fast need it urgently...

Homework Statement Given that the tangent to the curve c(t) at any point on the curve is T(t) = (-sin(t), cos(t) ), find c(t) if the curve passes through the point (0,0) .The Attempt at a Solution I try to let c(t) = ( x(t), y(t) ) Then c'(t) = ( x'(t), y'(t) ) | c'(t) | =...

Hello, it is mentioned http://en.wikipedia.org/wiki/Atan2#Definition" that using the tangent half-angle formulas it is possible to express the function atan2 as: \mathrm{atan2}(y,x)=2\mathrm{arctan}\frac{y}{\sqrt{x^2+y^2}+x} How can I derive this result?

Homework Statement My cubic function is y=(x-6)(x-1)(x-9) or y=x^3-16x^2+69x-54 I need to find the tangent at the point x=2.5Homework Equations The Attempt at a Solution All that I have managed to do is work out the y value for x=2.5, that is y=34.125 Please help someone!

Here's something simple but also a bit puzzling, let me know if you have any ideas... For clarity, I'll describe three cases before asking the final question (skip ahead if you like). 1. Mounted on a disk are two curved fences, just a few centimetres apart from each other. Between the fences...

Equation of tangent line (rec. form) to a polar curve! Homework Statement Quesiton: Find the rectangular form of the equation of the tangent line to the polar curve r=cos^3(theta) at the point corresponding to theta=pi/4 Homework Equations The Attempt at a Solution How to...

Not sure I understand exactly what this question is asking. This is obviously a volume in R3 and so how do you get a tangent inside a volume? Or is it just along the plane y = 2 intersecting the volume? Also, what is a parametric equation...? Thanks for the help: Question: The ellipsoid 4x^2...

Homework Statement A curve is given by the equation: y^3+1004=(e^x+1)^2 Find the slope of the tangent line at the point (0,-10). Homework Equations The Attempt at a Solution I took the derivative of ((e^x+1)^2-1004)^(1/3) and that is (2e^x(1+e^x))/(3((1+e^x)^2-1004)^(2/3)) but...

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...

Homework Statement Determine the equation of the tangent line and the equation of the normal line to the curve y at the point (-2,-5) y=1+x+x^2 The Attempt at a Solution y=1+x-x^2 point (-2,-5) y=1+x-x^2 y=1-2x sub in -2 for x...

It puzzles me. In Einstein's paper on the photoelectric effect he proposed that photons with E = nhf were the explanation. Wouldn't a more elegant explanation be that the tangent of the electromagentic wave must take on discrete values because of the boundary conditions between the emitter...

Homework Statement Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x2+y2 at the point (1, 2, 5) Homework Equations Gradients, Cross products The Attempt at a Solution I'm pretty lost here. I think I have to...

Can anyone help me with this problem?? Let M be a surface in R^3 oriented by a unit normal vector field U=g1U1+g2U2+g3U3 Then the Gauss map G:M\rightarrow\Sigma of M sends each point p of M to the point (g1(p),g2(p),g3(p)) of the unit sphere \Sigma. Show that the shape operator of M is...

Homework Statement Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 9sin(θ) θ = pi/6 Homework Equations dy/dx = (dy/dθ) / (dx/dθ) x=rcosθ y=rsinθ (sinx)^2 = (1/2)(1-cos2x) (cosx)^2 = (1/2)(1+cos2x) 2sinxcosx = sin(2x) The Attempt at...

I was working on a problem, and in my solution I came across a situation which I will try and state in the following question: Given two functions, f(x) and g(x), how would you find a line such that the line is tangent to f(x) at some point x=a, and tangent to g(x) at some point x=b, assuming...

Homework Statement If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2,-2), then f'(1) is? Answer: 3 Homework Equations The Attempt at a Solution I got the right answer, but I think it was by pure luck. I found the slope...

Homework Statement Write an equation of each horizontal tangent line to the curve. Homework Equations y = 2y^3 + 6x^2y - 12x + 6y = 1 y' = (4x - 2xy) / x^2 + y^2 + 1) The Attempt at a Solution Well, horizontal tangent line means the derivative equals zero. Thus, 4x - 2xy = 0...

Homework Statement Write an equation for the line tangent to the graph of f at x = 1 and use it to approximate f(2.1). Homework Equations y = mx+b f(1) = 4 f'(x) = (3x^2 + 1) / 2y m = 1/2 when x = 1 The Attempt at a Solution Well, if the line is tangent to the graph of f at x...

Homework Statement Let f be the function given by f(x) = 3e^2x and let g be the function given by g(x) = 6x^3. At what value of x do the graphs of f and g have parallel tangent lines? a. -0.701 b. -0.567 c. -0.391 d. -0.302 e. -0.258 Correct answer is c. -0.391 Homework...

We know that the slope of the tangent line at a point on a curve is found by evaluating the derivative of the curve at that point. Say we have the curve y=2x. Say I wanted to find the tangent line at x=4 dy/dx=2 The first derivative is a constant, which is not surprising since the curve is...

Homework Statement There are infinitely many points on the curve y = \frac{sin x}{\sqrt{2}- cos x} at which the tangent line to this curve is horizontal. Find the x- and y-coordinates of one such point. Homework Equations y' = slope of the tangent line Etc., etc. The Attempt at a...

Find which value of x...horizontal Tangent Line Homework Statement What is given is F(x)= -4/(x-3)(x+4) and the problem asks for to find the value of x where f(x) has a horizontal tangent line.Homework Equations I read somewhere else on these forms that using the quotient rule is the key, and...

Hi here in like thi9s queation we use ( Rad ) or (deg ) in the calcolator ?

Homework Statement Find all points on the curve x^2 * y^2 + xy = 2 where the slope of the tangent line is -1. Homework Equations y' = -1 The Attempt at a Solution I got the y' = [ -2xy^2 - y ] / [ 2x^(2)y + x ] to be the gradient which I am sure is right. Then I subbed in y' =...

Homework Statement Find the points on the lemniscate: 2( x^2 + y^2 )^2 = 25( x^2 - y^2 ) where the tangent is horizontal Homework Equations Horizontal tangent: y' = 0 The Attempt at a Solution I got the correct gradient of y' = [ 50x - 8x^3 - 8y^2 ] / [ (8x^2)y + 50y + 8y^3 ]...

This may seem like an easy question, but my differential geometry is a little rusty. I'm trying to find the tangent space to the Lie group U(n) ; that is, for an arbitrary X \in U(n) I'm trying to find an expression for T_X U(n) . I can't quite remember how to do this. I've been playing...

Greetings, Given three points P1 P2 P3 on a circle in x,y,z coordinates, I am trying to figure out how to get the tangent and normal at P2. Anyone? Thanks

hey there, i got stuck on an question here: Parameterise the following paths, in the dirction stated, and hence find a tagent vector(in the same dirction) to each point on the paths. (a)The upper part of the circled centred at (0,0) containing the points (-2,0) and (2,0) going anticlockwise...

Most functions y=f(x) have tangent lines for any point x. Does a function z=f(x,y) have a tangent plane for any point x,y? And could you extend this to higher dimensions if necessary? (Tangent cubes? Tangent hypercubes?) Edit: Sorry, I thought I was posting in the General Math forum...

suppose the function F is define by F(x)=[integral from 1 to √x] (2t-1)/(t+2)dt for all real numbers x≥0 A.) evaluate F(1) B.) Evaluate F'(1) C.)Find an equation for the tangent line to the graph of F at the point where x=1 D.) on what intervals is the function F increasing? justify your...

Homework Statement Surface (s) given by x^3*+5*y^2*z-z^2+x*y=0 question ask to find normal and tangent plane to S at the point P=(1,-1,0) then find vector tangential to curve of intersection of S and the plane x+z=1 at point P. Homework Equations The Attempt at a Solution So I started off...

Homework Statement If the equation of one tangent to the circle with center at (2, -1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is: (a) 3x - y = 0 (b) x + 3y = 0 (c) x - 3y = 0 (d) x + 2y = 0Homework Equations An equation of the tangent to the...

At what point on the paraboloid y=x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1 ? Tangent plane equation is... Fx(X,Y,Z,)(x-X)+Fy(X,Y,Z)(y-Y)+Fz(X,Y,Z)(z-Z)=0; for x^2+z^2-y=0 My attempt at the problem... First I found the unit normal for the plane I'm trying to...

Homework Statement tan(2x) - 3 cot (2x) = 0 Homework Equations Trigonometry Knowledge. The Attempt at a Solution tan(2x) - 3cot(2x) = 0 tan(2x) - 3/tan(2x) = 0 [tan(2x)]^2 - 3 = 0 [tan(2x)]^2 = 3 Is there such thing as Arc Tangent that's squared??

Homework Statement For every x>-4 where x\in \Re applies sinx+x\leqf(x)\leq8\sqrt{x+4}-16 Find the gradient of the tangent to the curve of f at x_{0}=0 Please help me I am trying to solve this exercise for more than two hours! I'm desperate.

Homework Statement Find the parametric equations of the line tangent to the curve of intersection of the paraboloid z = x² + y² and the ellipsoid 4x² + y² + z² = 9 at the point ( -1, 1, 2 ). Homework Equations Probable use of the gradient vector (as this is the chapter we are in)...

Help me understand exactly what is going on here. I'll put up an attempt at my solution: Find the tangent lines at the pole r = sin5o, [0,pi] (note: o represents theta) Equation: dy/dx = [f'(o)sino + f(o)coso]/[f'(o)coso - f(o)sino] f(o) = sin5o f'(o) = 5cos5o plugging everything...

Homework Statement is it possible to have a tangent line in a cubed function Homework Equations The Attempt at a Solution

Homework Statement find the slope of the tangent line of f at the given point. Homework Equations f(x)= x^3 + x at (2,10) The Attempt at a Solution I know how to get the answer using the power rule, but I want to know the algebraic way of doing it I get stuck at x^3 + x - 10/ x...

HALP! I have already killed a forest trying to work this one out on paper. Homework Statement a. Use Implicit differentiation to find the equations of the horizontal tangent lines to the parametric equation: yx^3-2x^2y^2+xy^3=192. b. Use Implicit differentiation to find the equations...

For what value of b is the line y = 10x tangent to the curve y = e^{bx} at some point in the xy-plane? y' = b*e^{bx} = 10x How can I solve for b here?

Homework Statement Find an equation for the line tangent to the curve at the point defined by the given value of t. x = 2 cos t y = 2 sin t t = pi/4 Homework Equations sin (pi/4) = sqrt(2)/2 cos (pi/4) = sqrt(2)/2 The Attempt at a Solution Determining the slope: [dy/dt]/[dx/dt]...

I am trying to find the exact value for tan(15). I figure my equation as 40 - 30 to give the 15. when deriving my equation is where I have the problem. can anyone help please. (1-√(3)/3)/(1 + 1 * √(3)/3)

Hi, I'm reading this piece from George Cain & James Harod's multivariable calculus material. Section 4.3, which is about Torsion, says this: I don't understand how he deduces dB/ds is perpendicular to T? Where did I get lost? Following the paragraph, it seems to me that T and N...

Alright, I'm having trouble with this problem, but I know that it's easy and simple. If the car starts at height h= 3.00 R and the radius is R_1 = 25.0 m, compute the tangential acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter...

Homework Statement 4x^2 - xy + y^2 = 4 At what points is the tangent line to the above curve vector [1 1]T? (T means I transposed the vector) Homework Equations The Attempt at a Solution I have the gradient vector, but I'm conceptually lost about what to do after that.