Tangent Definition and 1000 Threads

Find the slope of the functions graph at the given point. F(x) = x / x-2 point (3,3) f(x+h) - f(x) / h is what we have to use to find the answer. so I've plugged it all in and have came to this.. ((3+h) / (3+h-2)) - 3 / h I need some help with my simplification...

Find an equation for the line tangent to the given path at the indicated value for the parameter. x(t)=4costi-3sintj+5tk, t=\pi/3 So what I did here was take x'(t) and then plugged in \pi/3 after that to get an equation containing i, j, and k. x'(t)= -4sinti-3costj+5k...

Homework Statement Find the unit vectors that are parallel to the tangent line to the curve y=2sinx at the point (\pi/6, 1). Thereafter, find the unit vectors that are perpendicular to the tangent line. Homework Equations The Attempt at a Solution I took the derivative of y=2sinx and...

Homework Statement I've done this problem about 5 times, several different ways following many different examples but I can't seem to find the right answer or even figure out how they got one of the answers (y answer is given) The Attempt at a Solution r(t) = (1+4*sqrt(t), t5-t...

This is a problem many of the grad students have probably encountered, it's in Chapter 0 of Riemannian Geometry by Do Carmo. Do Carmo proved that the tangent bundle of a differentiable manifold is itself a differentiable manifold by constructing a differentiable structure on TM, where M is a...

Homework Statement http://img214.imageshack.us/img214/4673/mathproblemnw5.png Homework Equations lim x->a\frac{f(a+h)-f(a)}{h} The Attempt at a Solution Ive tried so many times to figure this out. I first substituted the equation into the formula above and multiplied by the...

Let f be the funtion given by f(x) = 4x^2 - x^3 , let L be the line y = 18 - 3x, where L is tangent to the graph of f. Show that L is the tangent to the graph of y= f(x) at the point x = 3. I'm equaling both graphs like this: 4x^2 - x^3 = 18 - 3x and then I isolate everything...

I have a position vs. time graph which is slightly curved. I found the slope of 2 tangent lines which I know are the velocity. My question is how do I get the acceleration using these 2 slopes. One slope is 295cm/s and the other is 575cm/s. I know that avg acceleration is final velocity -...

Homework Statement find the first four nonzero terms in the power series expansion of tan(x) about a=0 Homework Equations \Sigma_{n=0}^{\infty} \frac{f^n (a)}{n!}(x-a)^n The Attempt at a Solution Well the series has a zero term at each even n (0,2,4 etc) for n=1 I got x, for...

Homework Statement You have a circle with the equation x^{2} + (y + 1)^{2} = 1. You can draw to two tangent lines to that circle that intersect the point (0,1) What are the equations of these lines? And you can't use any calculus, derivatives and the like. Homework Equations y=mx+b...

A tangent to a curve is a line that touches the curve but at what specific point where there is a slope to the curve. Equations like y = X^2 have many slopes because the curve is shaped differently at different points. We can choose 2 points on the graph and find the slope but it will...

Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 950 in chapter 13.7 in the text, number 46. It...

The problem: The y-intercept of the line tangent to y=(x4-2x2-8)ecosx2 at x=1 is (a) -15.499 (b) -25.999 (c) -41.448 (d) 15.449 (e) 25.99 To find the y-intercept I have to find the whole equation of the line y=f(1) m=f'(1) x=1 b=?? My problem is that I don't think I got the the...

Homework Statement I have two problems that don't seem to match. The task is to find the parametric equation for the normal line to the tangent plane. I'm seeing that the vector value of "z" is (-1) with one formula, but not in the other. These two seem to be the same, but the first was solved...

Homework Statement Find an equation of the tangent line to the curve y = 5x3 at the point (-3,-135). Enter your equation in y = form. Homework Equations The Attempt at a Solution Taking the derivative of the equation I get y = 15x2, following that I plug in the x value of...

Two circles of radius 3√2 are tangent to the the graph y^2 =4x at (1,2). Find the equation of each circle. I have found the derivative of the graph, which is 1/√x. I know that the equation of the circle is X^2 + Y^2=r^2 where r is the radius so the equation of each circle is X^2 + Y^2=18...

Solve: lim x->0 (tan 3(x+h)-tan(3x))/h i hv no clue where to start =(

Homework Statement Find the equation of the tangent line to the graph of x^2 - xy + y^2 = 19 (where y=y(x)) at (3,-2). Homework Equations The Attempt at a Solution So, this is what I did: d/dx(x^2-xy+y^2) = (19)d/dx 2x*dx/dx-dy/dx+dy/dx+2y(dy/dx)=0 2x+2y(dy/dx)=0 And I...

Homework Statement Find equation of the tangent line at t=0 x=2sint y=tant The Attempt at a Solution Really don't know where to start, can someone give me the hint, don't solve it, i want to try it, just need a hint

Homework Statement I have the circle of equation (x-3)² + (y-4)² = 5² Find the exact length of the tangents from the point (10,0) to the circle Homework Equations The Attempt at a Solution Honestly I can't acutally visualise on a co-oridinate graph what it's asking. A tangent...

Hi, I'm studying for my pre-calc test tomorrow and I've run into a snag. I just can't seem to get the correct answer for a Tangent sum problem, and I'm hoping someone could help me out with it. It goes like this: Sum Formula for Tangant: Tan (a+b) = Tan a + Tan b/1-Tan a * Tan b Problem...

Circle: (x-2)² + (y+1)² = 25 Point A: (11,8) Therefore Center of Circle = (2,-1) and Radius = 5 Looks somewhat like: O> Basically there are two tangents coming from the edge of a circle with the above equation to a point (pt. A). I have figured out to make two right triangles by...

Verify that (1,1) is a point on the graph of y + ln xy = 1 and find the equation of the tangent line at (1,1) to this graph how do you go about answering this?

Homework Statement Find the smallest positive value for `theta` for which the tangent line to the curve `r = 6 e^(0.4 theta)` is horizontal The Attempt at a Solution I tried to use the (r'sin(theta)+rcos(theta))/(r'cos(theta) - rsin(theta)) formula to get the tangent line, which I got...

Proof: Everywhere Tangent to Curve?? If the function v depends on x and y, v(x,y) and we know there exists some function psi(x,y) such that v[SIZE="1"]x = partial w.r.t (y) of psi v[SIZE="1"]y= -(partial w.r.t (x) of psi) show that the curves psi(x,y) = constant, are everywhere tangent to v.

i have 2 simmilar questions 1) Find the equation of the line tangent to the curve at the point xy + y = 2 ; (1, 1) and i did this xy + y = 2 y + xy' + y' = 0 xy' + y' = - y y'(x + 1) = -y y' = -y/(x + 1) y' = -1/2 y- y_1 = m(x - x_1) and i hope so this is OK but how can i...

Can someone help me with this problem? Consider the curve defined by y=x/(x+1). (1,2) is a point NOT on the curve. Find the equations of the two tangent lines to the curve passing through the point (1,2).

[SOLVED] Tangent plane to surface Homework Statement Find an equation for the tangent plane to the surface z^2 = x^2 + 2y^2 at the point P = (1,2,3). Which other points on the surface have the same tangent plane? 2. The attempt at a solution I find the derivatives: fx =...

using those formulas, how would you solve tan 11 pi ----- 8 and cot 195 also, how would you prove tan (x +y ) = tan x and tan ( pi/4 -x) = 1 - tan x --------- 1 + tan x thank you so much for any help

Homework Statement Let bar r(t) = < -1t^(2)+2, -3e^(5t), -5sin(-4t) > Find the unit tangent vector `bar T(t)` at the point `t=0` The Attempt at a Solution Attempt: r(t) = -1t^2 + 2, -3e^5t, -5sin(-4t) v(t) = -2t, -3e^5t, -5cos(-4t)*-4 T(t) = (-2t - 3e^(5t) -...

What exactly are the tangent and the normal accelerations of a projectile motion and how are they expressed mathematically? What is curvature radius? What is its expression? How is it derived ?

Two surfaces are said to be tangential at a point P if they have the same tangent plane at P . Show that the surfaces z = √(2x²+2y²-1) and z = (1/3)√(x²+y²+4) are tangential at the point (1, 2, 3). differentiate first then evaluate both at 1,2,3

Homework Statement Find all points on the graph of the function at which the tangent line is horizontal. f(x) = 2sinx + (sinx)^2 Homework Equations Hi guys I have an issue. I do not know how to approach this problem. I know the chain rule but I still do not know how to solve the...

Help my guys. I'm so hopelessly lost on this question... Problem: Determine the equation of the tangent to the graph of y=ln x that has slope e. The answer in the book is y=ex-2. Please help. :smile:

Homework Statement The equation of tangent is given t:2x+3y-2=0 and the equation of elipse E:x^2+4y^2=K Find "a" and "b" and the coordinates of touching point D. Homework Equations equation of elipse: b^2x^2+a^2y^2=a^2b^2 equation for touching: a^2k^2+b^2=n^2 equation for K (if...

Homework Statement Find the equation of the tangent of the circular K:x^2 + y^2 - 2x + 4y=0, perpendicular to the line x-2y+9=0. Homework Equations (x_1-p)(x-p)+(y_1-q)(y-q)=r^2, equation of K. (kp-q+n)^2=r^2(k^2+1), condition for tangent and circular K The Attempt at a Solution...

The problem is to find the horizontal tangent lines of an equation. Here's my attempted differentiation. y^2 = x^3 - x + 1 {dy/dx} = (3x^2 - 1)/(2y) Correct, or no? i'm going to need more help going forward even if that is right, I just want to make sure it is.

For which value of x...horizontal Tangent Line Homework Statement For which value of x does f(x) = \frac{k}{ax^{2}+bx+c} have a horizontal tangent line? Homework Equations Quotient Rule? F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2? The Attempt at a Solution Am I supposed to...

Homework Statement At which point is the tanget line to the following curve horizontal? y= a sin^{3}\theta x = acos^{3}\theta Homework Equations The Attempt at a Solution \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} When \frac{dy}{dx} = 0 , this means that that the tanget...

Is it possible to have a tangent vector field on the unit 2-sphere x^2+y^2+z^2 =1 in 3D which vanishes at exactly one point? By the Poincare-Hopf index theorem the index of such vector field at the point where it vanishes must be 2. Is that possible? If yes, can one write an explicit formula...

Homework Statement Find the point on the parabola y= 4x^2 + 2x - 5 where the tangent line is perpendicular to the line 3x + 2y = 7. Homework Equations The Attempt at a Solution I don't know what to do since I was away the last 3 classes since I was away. Help me please.

Slope of a tangent = limit of the function? Hi. I want to ask . Can it be true that The slope of a tangent line is a limit of a function. or The slope of a tangent line can be considered as a limit of a function? ? Is it the same I mean the slope of a tangent line and a...

I have encountered a problem in my Calculus homework. I have a position function, r(t)= (t^2)i + (4t)j and in my homework, I am asked to find the tangent to this curve at the point t=3. I did this by finding dy/dx, or 2t/4 @ t=3 is 6/4. However, I am also asked to relate this to the...

Given equation x^2/9 + y^2/4 = 1. Determine the two points on the ellipse having a tangent line passing through the point (0,3). Cant seem to figure this one out? I have found the derivative of the slope which is -4x/9y. I don't know how to use that slope in order to find a tangent line that...

Affine spaces can be regarded as smooth manifolds if we take the natural topology and affine coordinate charts as atlas. So, if M is an n-dimensional affine space, then the tangent vector of a curve C: [0,1] \rightarrow M in a point p = C(t_0) can be defined as a derivation (as in any smooth...

Dear all, I can formally understand one of the many definitions of tangent vectors to a manifold, but what are they in reality? It should depend on the nature of the points of the manifold, for example, if M={set of events of general relativity}, then vectors are velocities. Other examples...

If cosine is equal to -12/13... Find sine and tangent in Quadrant If cosine is equal to -12/13... Find sine and tangent in Quadrant Two... What is the answer??

Find the tangent lines to the ellipse x^2 + 7y^2 = 8 at the point (3,0) Slope-intercept form: y=mx+b I know you have to differentiate the equation implicitly to get the slope, but you come across a zero in the denominator and that has me stumped.

1. Find the equations of all tangents to the graph f(x) = x^2-4x + 25 that pass through the origin. 2. The relevant equations to my knowledge are the slope formula and f ' (x) 3. First I found the derivative using various rules to be f ' (x) = 2x - 4 after this i used the slope formula and my...