Tangent Definition and 1000 Threads

Hello, I'm having trouble understanding an example from my test and I would appreciate your help clarifying how to get from one step to the next. Problem: Find an equation of the tangent line to the hyberola y = 3/x at the point (3,1) Eqation: m = \frac{f(a+h) - f(a)}{h} m =...

Hi, I'm having trouble plotting the tangent line on a curve (or the derivative evaluated at a point) in spice. I know how to plot the derivative of the entire curve using the d() function, but I don't know how to evaluate it at a point. Any help is much appreciated!

I need someone to help me! i have been given a center point of (3,-1,-2) of a sphere and i need to get an equation for when it is tangent to the a) the yz plane b) y=7. i know i need to use the distance formuala to attain the radius, but i am majorly confusing myself in what coordinate to pick...

If the tangent line to y = f (x) at x = a is the same as the tangent line to y = g(x) at x = b, find two equations that must be satisfied by a and b. I don't understand how to go about this problem. I tried putting the equations of the tangent lines together using the variables in the...

Homework Statement Solve the following limit: \lim_{x \rightarrow 1}(1-x)\tan{\left(\frac{\pi x}{2}\right)} The Attempt at a Solution I solved it using L'Hospital rule, it's equal to 2/pi, but is there any other way how to solve it? thanks a lot! The same question would apply to \lim_{x...

Sorry title was supposed to be Conic Sections, but my I key is sticky :) I had a question today, It went somethng like this: An epllipse of equation ((x^2)/4) + y^2 = 1 Find the equation of the tangent which passes through point P: (4,0) Well this was a mock exam question, where no answers...

Sorry if the title is a bit vague :/ The Problem: Find the point on the parabola y=1-x^2 at which the tangent line cuts from the first quadrant a triangle with the smallest area. Relevant Equations: y = 1-x^2 ; y' = -2x ; A= 1/2bh I'm basically stuck near square one, I found...

Find \mathop {\lim }\limits_{x \to 0} \frac{{\tan (nx) - n\tan (x)}} {{n\sin (x) - \sin (nx)}}

Homework Statement The point P (1/2, 0) lies on the graph of the curve of y=sin(2x-1) Find the gradient of the tangent to the curve of P Homework Equations ...I don't know The Attempt at a Solution I don't know where to start with this problem

Q: find the tangent to y = 9e^(2x)cos(pi*x) at (0,9) I know how to do the tangent for a polar coordinate at an angle, but how find it at (0,9)?

1. The problem statement, all variables and given/known i have to find all tangent lines in the equation below that pass though the point (0,0) y=x^{3}+ 6x^{2}+8i took the derivative and got this. y=3x^{2}+12x then i substituted the points x=0 and y=0 into the derivative equation and the...

Homework Statement if the tangent line to the graph of y=f(x) at (2.3) has an equation x-y+1=0, then f'(2) =? The Attempt at a Solution We did these problems in one small session at the beginning of the semester, but my notes aren't clear and I am not sure where to begin. Do I just...

Homework Statement I'm supposed to prove, that when G is a Lie group, i:G\to G is the inverse mapping i(g)=g^{-1}, then i_{*e} v = -v\quad\quad\forall \; v\in T_e G where i_{*e}:T_e G \to T_e G is the tangent mapping. Homework Equations I'm not sure how standard the tangent mapping...

What kind of tangent distributions are not integrable? Is there concrete examples with two dimensional non-integrable distributions in three dimensions? When I draw a picture of two smooth vector fields in three dimensions, they always seem to generate some submanifold, indicating integrability.

Homework Statement Let f be the function given by f(x) = (2x-5)/(x^2-4). a.Find the domain of f. b.Write an equation for each vertical and each horizontal asymptote for the graph of f. c.Find f'(x). d.Write an equation for the line tangent to the graph of f at the point (0,f(0)). The...

Homework Statement The tan(theta)=2/5 Homework Equations The Attempt at a Solution I forgot how, I had no clue so I looked in the solutions and it was 2.62 radians, I just don't know how they got that, I am not sure on what to do. Its for trigonometric forms of complex numbers...

Ok, I'm pretty much at whit's end trying to figure this review question out. Apparently my teacher forgot to mention that our book couldn't teach us everything we need to know for our test... Anyhow, the question is as follows, and I'm utterly at a loss as to what the answer is: Find the...

Homework Statement 1. Let f be the function defined by f(x) = -2 + ln(x^2). a) For what real numbers x is f defined b) Find the zeros of f c) Write an equation for the line tangent to the graph of f at x=1 Homework Equations The Attempt at a Solution a) all...

Here is what the question asks: Find the coordinate of all points in the graph of y=3e^x - x^3 at which the tangent line passes through the point (1,0). ---------------------------- I am told that the 2 points are (-.872, -1.027) and (2.275, 13.657). Any help at all that you can give...

Tangent space of single layered hyperboloid Ok i´m given a single layered hyperboloid given by \left(\frac{x}{a}-\frac{z}{c}\right)\cdot\left(\frac{x}{a}+\frac{z}{c}\right)-\left(1-\frac{y}{b}\right)\cdot\left(1+\frac{y}{b}\right)=0 Now the Problem asks me to take this as a vanishing...

My book really doesn't go into a lot of depth but I was wondering if this is correct If we are asked to find the tangent line of a specific value of t for a given parametric equation then we can find the equation of the tangent line in either rectangular or parametric functions. Rectangular...

i would like to know if my answer is correct can someone tell me the results for this: Find the equation of the tangent line to x^3-2x^2y+y^2=17 at (2,-1) ive gotten y'=(3x^2+4xy)/(-2x^2-y) and my line equations is y+1=(-1/4)(x-2) thanks in advance

[SOLVED] Integration of Inverse Tangent Function \int \frac{e^{x}}{4+9e^{2x}}dx Saw the problem, looked at it for a bit. Noticed that it is a inverse Tangent function. Played with some integration by parts and substitution and couldn't figure it out. Can anybody toss me a starting point on...

Why are the tangent vectors of smooth manifolds defined as mappings C^{\infty}(p)\to\mathbb{R} that have the similar properties as derivations? If a manifold is defined as a subset of some larger euclidean space, then the tangent spaces are simply affine subspaces of the larger space, but if...

Homework Statement \int {\frac{{dx}}{{\sqrt {x^2 - 2} \left( {x^2 - 1} \right)}}} Homework Equations \frac{d}{{dx}}\arctan (x)The Attempt at a Solution \frac{d}{{dx}}\arctan (x) seems to be part of it, I can't quite get much farther...

There is a base-quadrilateraled pyramid ABCDS , which base is quadrilateral ABCD. Inscribed sphere is tangent in point P on the ABCD wall. Proof that <)APB+<)CPD=180' I don't like geometry and i really don't know how to start.

Homework Statement y = 9sin(x)cos(x) Find all points where tangent line is horizontal. The Attempt at a Solution I get y' = 9cos^2x - 9sin^2X I plug in zero for the slope and get 9 but I'm stumped after that. How can I get all the horizontal tangent line points?

Homework Statement Find the tangent line to the curve y^2 (y^2 - 4) = x^2 (x^2 -5) at the point (0,-2). Homework Equations y-y1=m(x-x1) The Attempt at a Solution I d/dx-ed both sides and was left with dy/dx=0 so y=-2 Does that seem right?

Find the equation of the line tangent to the curve at (5, -3) (x-2)^2 + (y+3)^2 = 9 I solved the derivative to be dy/dx = ((-2x+4)/ (2y+6)) when i plugged in the points (5, -3) I got the slope as -6/0...How is this possible?? How can i find the equation of this curve if the slope is...

This is a general question, but what is the difference between finding the linearization and the tangent line to the same curve? And what about at a specific point?

Let \tan_1x=\tan x and \tan_{k+1}x=\tan\tan_kx. It's fairly clear that the sequence (\lfloor\tan_n1\rfloor) = http://www.research.att.com/~njas/sequences/A000319 is chaotic, in the sense that it can diverge from (\lfloor\tan_n(1+\varepsilon)\rfloor) even for small \varepsilon. 1. Any...

[SOLVED] Derivative and tangent line Homework Statement y = (x)/(x+x^-1) Find an equation of the tanget line to the graph at x=2 Homework Equations The Attempt at a Solution I used the quotient rule and got the derivative to be 0 / (x+x^-1) = y' so then the slope is 0 of the...

[SOLVED] Tangent Line Homework Statement Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3) Homework Equations The Attempt at a Solution At first I thought I knew how to do this problem, I found the derivative of the equation got: y' = 2x ; then...

Find an equation for the tangent to the curve y=1/(x-1) that has slope -1.

I'm not getting the right answers for sine, cosine and tangent functions. I have no idea why this is.

[SOLVED]Sine, Cosine and Tangent Trig Help I'm in 10th grade, I was just doing my homework when this dawned on me: How would one find Sine, Cosine and Tangent without a calculator. So if I am stuck in the desert with a stick I could find the Cosine of 73º by stick and sand method...

Homework Statement Find parametric equations for the tangent line to the curve x= t^4, y= t^4, z=t^3 at the point (1,1,1) Homework Equations The Attempt at a Solution I understand everything about solving this problem with the exception of how to find what t =? to plug in. ie...

Homework Statement suppose y=2x-3 is an en equation of the tangent line to the graph of y=f(x) at the point where x=2. find the value of f'(2) and f(2). Homework Equations I know how to get the tangent line, but this wording throws me off. a little help at how to solve f(2) and f'(2)...

Homework Statement Show that x+2y=7 is a tangent to the circle x^2+y^2-4x-1=0 Homework Equations The Attempt at a Solution One way would be to solve simultaneously by substituting for x or y and getting a perfect square showing that there is only one point of intersection. Is...

Homework Statement f(x) = |sinx| for - π ≤ x ≤ π g(x) = x^2 h(x)= g(f(x)) 1. Find domain and range of h(x) 2. Find an equation of the line tangent to the graph of h at the point where x= π/4 Homework Equations The Attempt at a Solution It think that h(x) is (|sin x|)^2...

Homework Statement Find an equation of the tangent line to the curve: 7*x*e^(x)+8 at (0,8) Homework Equations Derivative I guess? The Attempt at a Solution I know you have to take the derivative of the equation given which I think is 7*x*e^(x) + 7*e^(x) Then you plug it...

Homework Statement find the equation for the tangent line. 1. (e^x)(cos x) where x=0Homework Equations plugged 0 into the equation, (e^0)(cos 0) and got 1 for the y-coordinate. so I got the points(0,1). For the slope, I derived the equation into -(e^x)(sin x). then i plugged 0 in and got 0 for...

what is the difference between a linear approximation and a tangent line? my understanding is that the linear approximation is that it uses the tangent line at (a, f(a)) as an approximation to the curve y = f(x). my question really is, then why in calculus I do they make an entirely separate...

As far as I know, the tangent space of a manifold at a point is often defined abstractly as follows. First, we define the germ of smooth real valued functions at a point a, which is the set of equivalence classes of smooth functions where two functions are considered equivalent if they are the...

Homework Statement Find the equation of the tangent at the point indicated y=3cscx x=pi/4 2. The attempt at a solution So to do the question you need a point (which I am given), the slope and then you need to substitute that all into y=mx+b. I believe I have differentiated...

Homework Statement Given: f(x)=x^2-4x+5 find equation for two lines that are tangent to the graph and pass through the point P(0,1)Homework Equations f(x)=x^2-4x+5 \frac{dy}{dx}=2x-4 Equation of the tangent line/s f(x)=f'(a)(x-a)+f(a) The Attempt at a Solution Just need to get started

I have a function. I am asked to find the equation of the tangent to the curve at (3, f(3)) I think I am just confused of notation, but what is it asking here? To find the points, don't you put in the x value into the first derivative and this gets the y value, and use the formula for an...

Homework Statement 5. Find parametric equations for the tangent line to the curve of intersection of the surfaces z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5). The Attempt at a Solution f(x,y,z) = x^2 + y^2 - z^2 g(x,y,z) = x^2 + 2y^2 + z^2 Partial derivz...

What is the difference between a normal line and a tangent line?

Homework Statement Find an equation of the tangent line to the curve at the given point. y = \frac{x - 1}{x - 2} , (3, 2)Homework Equations m = \lim_{h\to 0} \frac{f(a + h) - f(a)}{h} y = mx + bThe Attempt at a Solution \lim_{h\to 0} \frac{\frac{(x + h) - 1}{(x + h) - 2} - \frac{x - 1}{x -...