Tangent Definition and 1000 Threads

Homework Statement Find all tangent lines of the graph f(x)=x+3/x that have a y intercept of 4. Homework Equations The Attempt at a Solution Assume a is the x coordinate of a point of tangency. Thus the point of tangency is (a, a+3/a). We know the tangent line must pass...

I know it sounds strange and abstract. and I've only come here as last resort because I couldn't find the answer on google. If I have y=Tan(x) how do I rearrange that so I have x=? It's probably a simple answer I've been overlooking, thank you for your time

Homework Statement Find the equation of y^2=x(x-3)^2 of tangent line at (3,0) Homework Equations Given above. I think implicit differentiation is involved or no since there is no xy's on the same side? The Attempt at a Solution Anyways... My attempt: 2ydy/dx = x*2(x-3)*1...

Here is the question: Here is a link to the question: Curve Tangent Question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement I've got the equation of a parabola y=2x^2-4x+1 with point (-1,7) and a tangent line running through it the point. I'm supposed to find the equation of the line. Simultaneously solve this equation with that of the parabola, place the results in form ax^2+bx+c, and find the...

1.Find the y-intercept of the tangent line to: y= -.4/√(3 + x) at [2.5, -.170560573084488] 2. So I thought the first step would be to find the slope of the tangent line. I think we find the slope of the tangent line by taking the derivative. So I am going to use the Quotient Rule to take...

Homework Statement Hi i have a circle that is shown by (x-7)2+(y+1)2=20 i also have a line y=2x-5 and i have to explain why the line is a tangent to the edge of the circle i know that the circle has the centre in (7,1) and that the radius of it is 4,4 Homework Equations i know...

In Stewart's calculus text, the way he derives the tangent plane equation at some point is to divide the general plane equation a(x-x_0)+b(y-y_0)+c(z-z_0)=0 by c This must mean c is always non-zero right? But isn't c is the 'z'-component of the normal vector to the surface at some point...

Homework Statement Show that: \frac{dx^\nu}{d \lambda} \partial_\nu \frac{dx^\mu}{d \lambda} = \frac{d^2 x^\mu}{d \lambda^2} The Attempt at a Solution Well, I could simply cancel the dx^nu and get the desired result; that I do understand. But what about actually looking at...

The circle x^2 +y^2 -4x+2y+m=0 is tangent with the line y=x+1.Find m. p.s : I know that o should solve it from the equations of two lines but i really get confused when i [FONT=sans-serif] substitute the y :/ . Thanx :)

I am trying to derive the equation of a tangent plane at some point (x_0, y_0) on a surface using vectors. This is how I have been trying to do it: The tangent line at (x_0, y_0) in the x-direction is z=z_0+f_x(x-x_0) so the vector parallel to it is L_1=<(x-x_0), 0, (z-z_0)>. Similarly...

Find the equation of the line tangent to f(x)= 3x^3 + 2 at x = 1. a) y = 9x-4 b) y = 9x+5 c) y = 3x 2 d) y = 3x+1 e) Not enough information given. Im confused on this one, but I am thinking about E, because it doesn't specify if the equation should be parallel or perpendicular to the...

I have been working through Spivak's fine book, but the part about differential forms and tangent spaces has left me confused. In particular, Spivak defines the Tangent Space \mathbb R^n_p of \mathbb R^n at the point p as the set of tuples (p,x),x\in\mathbb R^n. Afterwards, Vector fields are...

Homework Statement Find f if f"(x)=12x2+2 for which the slope of the tangent line to its graph at (1,1) is 3.Homework Equations The Attempt at a Solution What I did first was found f(x)=x4+x2+cx+d (cx and d being constants of integration.) and from this point I attempted solving for cx and d...

I am asking for simple guidance on this problem. f(x) = 3x^2-1, (2,11)I do believe I need to obtain an equation for tan line so first step I think is to use point slope or slope intercept (a friendly reminder to the name of formula would be very nice :)) y - ysub1 = m(x-xsub1) = y -...

Homework Statement The equations ##2x^3y+yx^2+t^2=0##, ##x+6+t-1=0## implicitly define a curve $$f(t) = \begin{pmatrix} x(t)\\y(t) \end{pmatrix}$$ that satisfies ##f(1)=\begin{pmatrix} -1\\1 \end{pmatrix}.## Find the tangent line to the curve when ##t=1##. Homework Equations The...

Homework Statement Find the tangent equations to the curve y^2= x-1/x+1 at the points with x=2 Homework Equations y=mx+b dy/dx The Attempt at a Solution I tried to solve in order to y: y=sqrt((x-1)/(x+1)) Then I derived to obtain the slope, but this is the part that I don't know if it is...

Homework Statement Find all points on the surface at which the tangent plane is horizontal z=x3y2 Things I know: Tangent plane is horizontal then therefore the normal must be vertical in order to be perpendicular. Dot product of the tangent plane with normal is = 0 Normal...

Homework Statement Find the equation of the tangent line of tan(xy2)=(2xy)/\pi at (-\pi,1/2) Homework Equations The Attempt at a Solution I managed to get the equation into its dy/dx form and for the slope to be (1-.5pi)/(2pi-2pi2) This seems far to complicated to be correct though.. can...

Homework Statement Find the points on the graph y=x^3/2 - x^1/2 at which the tangent line is parallel to y-x=3. Homework Equations The Attempt at a Solution First I found that the derivative of y=x^3/2 - x^1/2 is 1x. I then rewrote the other line as y = 3+x and found the...

Hi I am currently using origin to plot my data and using their fitting options I am able to get r square .98. Now I need to know slope at different positions of the curve even at x= 0. I tried one of their plugin and it gives me only three decimal point and which is not good enough. Could...

Homework Statement The tangent lines of two circles intersect at point (11/3,2/3). What are the two points that each tangent line touches on its respective circle? Homework Equations Circle 1: x^2 + (y-3)^2 =5 Circle 2: (x-2)^2 + (y+3)^2 = 2 The Attempt at a Solution I found the...

Homework Statement \frac{3x+6}{2-x} at x=3 Homework Equations y - y_{o} = m(x-x_{o}) The Attempt at a Solution f(3) = -\frac{15}{4} m = \frac{3}{0} DNE I have to write the equation in the form of the point-slope formula. I can get x_{o} and y_{o}, but I am...

Homework Statement Find the equation of all straight lines, if any, that are tangent to both the curves y = {x^2} + 4x + 1 and y = - {x^2} + 4x - 1.Homework Equations The Attempt at a Solution Suppose such a line exists and its slope is m. Let ({x_1},{y_1}) and ({x_2},{y_2}) be the tangent...

Graphics3D[Sphere[{0, 0, 0}]] How do I add a tangent plane and normal vector to this plot? I am not opposed to Matlab or Latex either.

Homework Statement Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P r(t)= <2sin(t), 2cos(t), 4sin2(t)>, P(1, √3, 1) The Attempt at a Solution I found T(t) using the formula T(t)= r'(t)/||r'(t)|| r'(t)= <2cos(t)...

OK, this looks like a differential geometry problem, which it is, but at the end of the day I am trying to figure out why the unit normal and unit tangent vectors to a curve aren't orthogonal, so even if you don't know about DG, please respond. Obviously the two choices for E_1 and E_2...

Does the function f(x) l x2-1 l have a tangent line at x=1? What is the tangent line if it does? Attempt: l x2-1 l (x2-1) When x ≥ 1 -(x2-1) When x < 1 Lim x→1+ (x2-1) = 0 Lim x→1- -(x2-1) = 0 Therefore, it does have a limit because the right and left hand limit are equal and the slope...

Homework Statement For what values of a are y=a^x and y=1+x tangent at x=0? Explain Homework Equations y1=1+x y2=a^x y2'=a^xln(a) y1'=1 The Attempt at a Solution Since both equations are tangent at x=0 i set their derivatives equal to each other in hopes of getting a a^xln(a)=1...

[a]Give a parametric equation for the line tangent to this curve at t = \frac{pi}{4}. \vec{r(t)} <e^tcost, e^tsint> Give the equation for this same tangent line in the form ax + by = c [b]My attempt \vec{r(\frac{pi}{4})} = <e^\frac{pi}{4}cos\frac{pi}{4}, e^\frac{pi}{4}sin\frac{pi}{4} =...

Hi there, The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$

This is confusing me more than it should. A curve in space is given by x^i(t) and is parameterized by t. What is the tangent vector along the curve at a point t= t_0 on the curve?

Homework Statement Determine the equation for the the tangent-to the curve: y=3 sin 2x - cos 2x if x=3∏/4 Homework Equations So I thought I might get the y? y=3 sin 2(3∏/4) - cos 2(3∏/4) y= ~0.25 - ~1 ≈ 0.75 k(?) = m(?) = Then what? Please help :( The Attempt at a...

Homework Statement The graph of y = f(x) passes through the point (9/2, 100/3). Also the tangent line to the graph at any point (x,y) has the slope 4*sqrt(2x+7). Find f(x)Homework Equations The Attempt at a Solution I am very lost with this as I can't find much info in my textbook. Any help...

I read the following on a page about atomic orbitals (p and d orbitals in particular) which seem 2 me like 3d lemniscates (figures 8 or ∞ rotated about an axis of symmetry to form tear drop pairs or toruses. http://www.chemguide.co.uk/atoms/properties/atomorbs.html Taking chemistry further...

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, ~x~\epsilon~[0, \frac{\pi}{2}] which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along...

Homework Statement Hello again. The question asks me to find an equation of the tangent to the graph: f(x)= - sin^2 x + 1/2, x \epsilon [0, \frac{\pi}{2} which makes an angle of 135° with the x-axis (measure anti-clockwise from the positive x-axis). Assume that the scales along the...

Working through intro GR at the moment and I'm a little unclear on how tangent spaces are used to carry four-vectors over from SR to GR. So, at every point in spacetime we construct a tangent space. We can form a basis for this space with the tangent vectors (i.e. the four-velocities) of one...

What is the equation of the circle with a center point of (10, -14) when the circle is tangent to x=13? D = √(13-10)^2 + (0-(14))^2 D = √(3)^2 + (14))^2 D = √9+196 D = √205 Radius = √205 (x-10)^2 + (y-(-14))^2 = √205^2 (x-10)^2 + (y+14)^2 = 205 But how am I suppose to graph this?

1. How many tangent lines to the curve \left(y=\frac{x}{x + 1}\right) pass through the point (1,2)? At which points do these tangent lines touch the curve? 2. \frac{x}{x + 1} 3. I tried to use the quotient rule and came up with the equation \frac{1}{(x + 1)^{2}}. I tried plugging in 1 to get the...

Homework Statement the tangent of the graph 1/x^2 at P(2,1/4) forms a triangle with the x and y axis. Find area of triangle.Homework Equations The Attempt at a Solution so f'(x)=-2/x^3 so the slope of the tangent at point 2, is f'(2)=-2/8 = -1/4=mt now i use the equation of the line to...

Hey guys, i'm building an apparatus with a sliding pin containing a spring and a ball. I want to lock in two different positions so I've rounded two slots in the housings. I would like to know what is the equation two find the normal force of the spring on the ball depending on the displacement...

Homework Statement The tangent to the function y=3x(x-3) at point P(2,-6) is the hypotenuse of a right triangle that forms with the coordinate axes. Find Area The Attempt at a Solution First of all, i know that i A=BxH/2 so i need the opposite and adjacent sides of this triangle...

Homework Statement r(t)=cos(t)i+sin(t)j+sin(2t)k Find the curvature κ, the unit tangent vector T, the principal normal vector N and the binormal vector B at t=0. Find the tangential and normal components of the acceleration at t=∏/4 Homework Equations T(t)=r'(t)/|r'(t)| N(t)=T'(t)/|T't|...

Hi all, I'm quite confused concerning the definition of tangent vectors and tangent spaces as presented in Munkres's Analysis on Manifolds. Here is the book's definition: Given ##\textbf{x} \in \mathbb{R}^n##, we define a tangent vector to ##\mathbb{R}^n## at ##\textbf{x}## to be a pair...

Dear all, in what sense the tangent space is the best approximation of a manifold? The idea is clear to me when we think about a surface in Rn and its tangent plane at a point. But what does this mean when we are referring to very general manifolds? In what sense "approximation" and in what...

Homework Statement This problem is 2.95 of University Physics, 11th edition. Catching the Bus: A student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it starts to pull away, moving with a constant...

Homework Statement Find an equation of the tangent line to the curve y = x√x that is parallel to the line y = 1+3x. Homework Equations m = 3 The Attempt at a Solution Here is my attempt: dy/dx(x) * dy/dx(x^(1/2)) = (1) * (1/2x^(-1/2)) = (1/2x^(-1/2)) (1/2x^(-1/2)) = 3 →...

Homework Statement Need to find the tangent to the curve at: e^(xy) + x^2*y - (y-x)^2 + 3 I just implicitly differentiate the expression to find the gradient and then use the points given to find the equation, right? Or does this involve partial differentiation? Homework Equations...

Homework Statement 1/(u^2+4) Homework Equations The Attempt at a Solution I know that 1/(x^2+1) is the derivative of the inverse tangent function, and that is proved by using tany = x, derivative of both sides with secx=(1+tan^2x) and tan^2x = x^2. I don't know how to use the...