Tangent Definition and 1000 Threads

Here are the questions: I have posted a link there to this thread so the OP can view my work.

Homework Statement I was given parametric equations. x(t) = a(t) y(t) = b(t) z(t) = c(t) where a, b, and c are functions that depend on t. I was supposed to find equation of the tangent line at t = f given: x(f)= m y(f) = n z (f) = o where m,n,o are some constant numbers...

I've looked at this topic for a while and I have yet to come to any sort of conclusive answer when it comes to calculating the basis of a surface's tangent vector. Do you have a concrete method or know where I can find one for doing this? Thank you

Homework Statement I'm trying to follow a solved example in the book. I understand everything except one "trivial" (for most of you) analysis of the tangent velocity vector v_b. Because v_b is unknown it is written as its magnitude times the direction it follows constrained in a circular...

Homework Statement Homework Equations I know the equations. See question below. The Attempt at a Solution I am just wondering with this problem, how is it that they go from that derivative to the magnitude at the bottom of that image? I know the formula, but what I mean is...

I need help getting around this Calculus 3 problem. Any hints will be gladly appreciated: Find the radius of smallest sphere that is tangent to both the lines L1 : x=t+1 y=2t+4 z=−3t+5 L2 : x=4t−12 y=t+5 z=t+17

Homework Statement Find an equation for the line y=(x^2)lnx at (1,0) Homework Equations The Attempt at a Solution I took the first derivative of the equation and got y'=2xlnx +x In other equations, it would be simple to find the slope, but at this point I am lost, is the slope 2...

Find the slope of the tangent line to the curve f(x)=x-x^3 at the point (1,0) So, I went through and plugged (a+h) in everywhere I saw "x" (a+h)-(a+h)^3 Factoring: (a+h-a^3-3a^2h-3ah^2-h^3) I'm really stuck on what to do next...I don't see anything you can cancel/pull out? I know...

Here is the question: I have posted a link there to this thread so the OP can view my work.

I am trying to self-study some concepts in differential geometry to try to update my knowledge from the old-style index games to something more meaningful. I know that there are many threads that have in some way addressed this, but I am still not understanding it completely. I'm new to this...

Hi all, this question stems from a homework question but is not the homework question itself, more a discussion on something I found, hence why I have put it here. The question involved using variational calculus to minimise the surface area of a soap bubble to find the shape it would take. The...

The equation of a tangent plane at the point (1/sqrt3, -1/sqrt3, 1/sqrt3) for a unit sphere with center at origin. I'm studying for an entrance and this is in the previous question paper MCQ. I've been trying to solve this by studying similar problems but somehow I think the solution here is...

Hello All, I have been trying to brush up on some calculus (differential, I haven't learned integral yet) on my own by finding whatever calculus problems I can find. Recently I found this question listed as a CLEP practice question, and have been having some difficulty with it. Here is the...

I'm a high school physics teacher trying to get a handle on differential geometry so please make explanations as simple as possible. What is the difference between the tangent space at p and the affine tangent plane at p?

Given the parametric equations, find an equation of the tangent line at the given point on the curve. Homework Statement Find an equation of the tangent line at each given point on the curve: x = 2cotΘ and y=2sin^{2}θ at point (\frac{-2}{\sqrt{3}},\frac{3}{2}) Homework...

find the equation of the tangent line.$$y = e^{3x + cos x}$$ @ x = 0 $$ y1 = e^{3(0) + cos(0)} = e^1 = e$$ $$y1 = e$$ $$y = e^{3x+cos x}$$ $$y' = e^{3x + cos x} * (3 - sinx)$$ $$m = 3e$$ $$ y - e = 3e(x - 0) $$

Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1 $$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$

This is my first post, and I'm excited to be able to receive quality help from what seems to be a good place. I'll attempt to start using the proper format and make it easy for everyone to read, thank you for the help! This should be a simple problem, but I seem to have forgotten how to do it...

Hello. In my textbook by Jose Saletan called Classical Dynamics: A Contemporary Approach the author talks about TQ, the domain of the Lagrangian. He states that the space tangent to a point on the configuration manifold is in the tangent bundle, and that the entire tangent bundle can be thought...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Tangent and normal parabola Homework Statement P is a point 't' on the parabola y^2=4ax and PQ is a focal chord. PT is a tangent at P and QN is a normal at Q. The minimum distance between PT and QN is equal to Homework Equations The Attempt at a Solution I think minimum distance will...

Just for fun, eh...? (Heidy)For $$z \in \mathbb{R}$$, and $$m \in 2\mathbb{N}+1$$, show that:$$\frac{\tan mz}{\tan z}=\prod_{j=1}^{ \lfloor m/2 \rfloor } \tan\left(\frac{j\pi}{m}+z\right) \tan\left(\frac{j\pi}{m}-z\right) $$

How does it look like if three unit vectors at a point such that each vector is tangent to one of the axes in 3-Dimensional Cartesian System? Can anyone illustrate about this? Thanks.

Hello, I understand the concepts of real differentiable manifold, tangent space, atlas, charts and all that stuff. Now I would like to know how those concepts generalize in the case of a complex manifold. First of all, what does a coordinate chart for a complex manifold look like? Is it a...

Hello, I notice that most books on differential geometry introduce the definition of differentiable manifold by describing what I would regard as a differentiable manifold of class C∞ (i.e. a smooth manifold). Why so? Don't we simply need a class C1 differentiable manifold in order to...

Homework Statement Problem: A curve given parametrically by (x, y, z) = (2 + 3t, 2 – 2t^2, -3t – 2t^3). There is a unique point P on the curve with the property that the tangent line at P passes through the point (-10, -22, 76). Answer: P = (-4, -6, 22) What are the coordinates of...

Homework Statement Is there any direct formula for calculating the direct common tangent of two circles without having to go all the trouble of using y-y1=m(x1-x2) to derive it for two separate tangents t1 and t2. If there is could anyone explain to me how it is derived? Homework...

Homework Statement Find the equation of the tangent drawn from the point(-5,4) to the circle x^2+y^2-2x-4y+1=0 Homework Equations y-y1=m(x-x1) x^2+y^2+2gx+2fy+c=0 The Attempt at a Solution The equation of the tangent using the point is as follows y-4=m(x+5). Now, if I substitute...

Homework Statement Find X. Given the following Equation2.094 radians =tan^-1(2*x*(1.11)/1-(1.11)^2) Homework Equations The Attempt at a Solution How do you get rid of inverse tangent? Here's what i got tan(2.094((180/pi))*(1-(1.11)^2) / 2*1.11 = X

Homework Statement Homework Equations The Attempt at a Solution So I am not sure how many times I tried this thing but the final answer is still wrong. I am sure it is something simple, where did I goof it? *and why do we call it a tangent plane?

Here is the question: I have posted a link there to this topic so the OP can see my work.

1. If an equation of the tangent line to the curve y=f(x) at the point a=2 where is y=4x-5, find f(2) and f'(2). Homework Equations [SIZE="4"]m=\frac{f(x)-f(a)}{x-a} The Attempt at a Solution To be honest, I really don't know where to start. Here's what I have so far...

hey all can anyone explain why, for small \alpha we may allow \tan \alpha = \alpha at an intuitive, geometrical perspective. i already understand the series explanation and higher order of tangent. I am just trying for a picture. thanks!

Hi MHB, I've come across a math problem lately and it seems so interesting to me but I don't understand the statement below, which caused me failed to think of a good method to solve it. "The line is tangent to the graph at exactly two distinct points." I understand that if we have a...

Homework Statement Consider the tangent surface of some regular differentiable curve given as X(t,v) = \alpha(t) + v \alpha'(t) . Show that the tangent planes along X(t,constant) are equal. Homework Equations N = \frac{X_{t} \wedge X_{v}}{|X_{t} \wedge X_{v}|} The general tangent...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Show that TS^1 is diffeomorphic to TM×TN. (TS^1 is the tangent bundle of the 1-sphere.) We can use the theorem stating the following. If M is a smooth n-manifold with or without boundary, and M can be covered by a single smooth chart, then TM is diffeomorphic to M×ℝ^n. Clearly, I must be...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement I need to use the following data table to: 1. make a position-time graph 2. draw tangents (it isn't specified how many, but a previous practice question only drew 3 out of a possible 5) 3. create a time-velocity table. 0 --- 0 0.25 --- 0.29 0.50 --- 1.15 0.75 --- 2.59 1.00...

Homework Statement Now use your answer from part (a)(This anwser is f'(25) = 7/10, which is correct) to find the equation of the tangent line to the curve at the point (25, f(25)). Homework Equations f(x) = 7*sqrt(x)+3 The Attempt at a Solution f'(25) = 7/10 f(25) = 38 y=mx+b...

Homework Statement Consider g(ξ) = [(2H)/π] arctan(ξ). Plot a graph of the function g(ξ). Imagine a line that passes through the point on the curve at ξ0 = 1.30, and which is tangent to the curve at that point. Where does the tangent line intersect the vertical axis? [DATA: H = 2.00 ; ξ0 =...

The line y = ax + b is tangent to y=x3 at the point P = (-3,-27). Find a and b. I'm pretty lost on this one. Here's my initial thoughts. Find (a) first. (a) is equal to the slope which is the derivative of x3 So (a) would be equal to 3(-3)2 ? Not quite sure where to start on this one.

Homework Statement I don't know how to make theta so ∅ = theta. find the slope of the tangent line at r = sin(6∅) when ∅ = pi/12 Homework Equations y=rsin(6∅) x=rcos(6∅) r=sin(6∅) tangent line equation y-y' = m(x-x') m = dy/dx The Attempt at a Solution when ∅ = pi/12 then...

Homework Statement Find an equation of the tangent to the curve given by x=tan(∅) y=sec(∅) at the point (1,sqrt(2)) The answer should be in the form y=f(x) without ∅ The Attempt at a Solution Tangent line equation... y-y*=m(x-x*) m = dy/dx m = sec(∅)tan(∅) / (sec^2(∅) m = tan∅...

Hi there, the problem says, an n-gon is circumscribed around a circle so the mid point of each side is tangent to the circle. Prove the triangle consisting of one side of the n-gon and the sides from the end points to the middle of the circle has area tan(pi/n) Cheers!

I don't need an answer, I'm just stumped as to how to properly turn these into point slope form to find the tangent, can anyone guide me through this? Help would be greatly appreciated. I believe I understand the formulas that are used to solve problems such as these. It starts by finding the...

For the curve defined by r(t) = 3*t*i + 2*t^2*j − 3*t^4*k Find the tangent vector r′(t0) at the point P(4,8,−16), given that the position vector of P is r(t0). and Find the vector equation of the tangent line to the trajectory through P. Im unsure as to how to go about solving this. I've...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement Calculate a function of theta that gives the slope of the tangent line (dy/dx) to the polar curve r at some angle theta. Homework Equations dy/dx= f'(theta)sin(theta) + f(theta)cos(theta)/[f'(theta)cos(theta) - f(theta) sin(theta)] The Attempt at a Solution I am...