Tangent Definition and 1000 Threads

Homework Statement Homework Equations The Attempt at a Solution

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers! Let f(x)=−3x+6 if x<-3 = 15 if x > -3 Find the average rate of change of f(x) on the interval −5<x<5 . The average rate of...

Hi a ) find an equation for the horizontal tangent to the curve y=x-3root x b) What is range of values of values of curve's slope ? c ) What is range of values of curve ? number a already I solved but my queation now in b and c ----- I try to solve b) to get curve's slope must...

Homework Statement A cyclist intends to cycle up a 8.2^\circ hill whose vertical height is 180 m. The mass of the bike and the cyclist is 95kg. If each complete revolution of the pedals moves the bike 4.7 m along its path, calculate the average force that must be exerted on the pedals...

Homework Statement Is it possible that there are two different tangent lines to this function that are perpendicular to each other? If so, find the equations of the two lines and show that they are tangent to ƒ(x) and perpendicular to each other. If not, show why it is not possible...

Homework Statement What must hold true for a function to have a tangent at the origin. Eg. Given f(x) = 0, x = 0 and f(x0 = xsin (1/x) x does not equal 0 will the graph have a tangent at the origin? Homework Equations The Attempt at a Solution

Homework Statement The ellipsoid 4x^2+2y^2+z^2=16 intersects the plane y=2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2) Homework Equations sin(t)^2 + cos(t)^2 = 1 The Attempt at a Solution After plugging 2 in for y, I get...

gradient vectors and tangent lines! If f(x, y) = xy, find the gradient vector f(3, 7) and use it to find the tangent line to the level curve f(x, y) = 21 at the point (3, 7). I already found the gradient vector to be <7, 3>, Maybe I am missing something obvious, but I have no clue how to...

Homework Statement Given a point P (3, 10) and the equation of a curve as x^2 -5x-4, find the slope of the secant and the equation of the tangent line to the curve Homework Equations The Attempt at a Solution I tried using y = f(x + h) -f(x) all divided by h and got (x + h)^2 -...

Homework Statement This is a very basic problem, though it did confuse me a little: Find the tangent equations to the curve x=3t^2+1 \ , \ y = 2t^3+2 which intercepts the point (4,3). Homework Equations --- The Attempt at a Solution I took \frac{dy}{dx} = t =...

Homework Statement find the equation on the tangent plane of yz=ln(x+z) at point (0, 0, 1 ) Homework Equations Tangent plane equation... The Attempt at a Solution I wasn't sure how to determine the partials on this equation. My attempt was to rearange as ln(x+z)-yz=0 so Fx =...

Homework Statement Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line. Homework Equations dy/dx dx/dy or something not sure. The Attempt at a Solution Well I know that a horizontal tangent line would mean the slope is zero...but what...

Homework Statement Hello, this is a problem from the practice test for the GRE subject test. For what value of b is the line y=10x tangent to the curve y=e^{bx} at some point in the xy-plane? A) \frac{10}{e} B)10 C)10e D)e^{10} E)eHomework Equations The Attempt at a Solution For the line to be...

I am terribly confused on the issue of trivial tangent bundles. I understand intuitively why some tangent bundles are trivial and others are not, but I'm having trouble figuring out how to show it. Even the most trivial example, show that T\mathbb{R}^n is diffeomorphic to \mathbb{R}^{2n} I...

Derivative and horizontal tangent help! Homework Statement Determine the point at which the graph of the function has a horizontal tangent line. Homework Equationshttp://www.webassign.net/cgi-bin/symimage.cgi?expr=f%28x%29%20%3D%20%288%20x%2A%2A2%29%2F%28x%2A%2A2%2B8%29and f(x)=x/...

Derivative and horizontal tangent help! Determine the point at which the graph of the function has a horizontal tangent line. http://www.webassign.net/cgi-bin/symimage.cgi?expr=f%28x%29%20%3D%20%288%20x%2A%2A2%29%2F%28x%2A%2A2%2B8%29 and f(x)=x/ root2x-1endroot

find all vertical tangent lines of a curve - more than one variable! curve : xy^2 - x^3y = 6 derivative : (3x^2y - y^2) / (2xy - x^3) question : find the x coordinate of each point on the curve where the tangent line is vertical. after some consideration, i decided that when the derivative...

Homework Statement Verify that (1,0) is on the following curve and find the tangent line and normal line to the curve at the point. y=pisin(pix-y)The Attempt at a Solution i think i got it is y ' {-1/pi*cos(pi*x-y)} + pi

Homework Statement We are given the unit circle and the point (5,2). There are two lines that are tangent to the unit circle and they both intersect at the point (5,2). What are the points where these lines are tangent with the unit circle. Homework Equations Tangent line of a circle at...

First Problem Homework Statement Find the derivative of x^6+y^6=18xy Homework Equations Find derivative The Attempt at a Solution 6x^5+6y^6=18*(dy/dx) Second Problem Homework Statement Verify that (1,0) is on the following curve and find the tangent line and normal...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at a given point. \[x = t^5, y = t^4, z = t^3\] at point (1,1,1) Homework Equations The Attempt at a Solution So we need to have direction vector, and a point. To find...

Homework Statement So, it's my understanding that there must exist a line which is tangent to a given circle and intersects a given point in 2D space. I'm trying to find that line. Any form will do, but I'm currently aiming for the coordinates of the two points: the intersection point, and the...

Homework Statement Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1) The Attempt at a Solution x3-y3=1 3y2(dy/dx)-3x2=0 3y2(dy/dx)=3x22 (dy/dx)=3y2/3x2 (dy/dx)=x2/y2 slope = (dy/dx) = 1...

Homework Statement Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16) Homework Equations The Attempt at a Solution dy/dx x2(x + 1)4 = (x + 1)3((x + 1)2x + 4x2) = (x + 1)3(6x2 + 2x) = (x + 1)3(2x)(3x + 1) Subst. 1 into find grad. (1 +...

Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is horizontal. Consider the domain x = [0,2π). f'(x)=2cos2x+2cosx

Ola, If we have two curves, and they cut them selves in a way like these two: y=x^2 and x^2+(y-1)^2=1. Does it always mean that those two curves in a cut point would have a same tangent, in other words do they need to have the same derivative in that spot? Thanks!

Homework Statement Find the equations of the tangents to the following graphs for the given values of x. (a) y = ln x, where x = 1/2 Homework Equations The Attempt at a Solution I know ln x differentiated is 1/x but I cannot see when the rest fall into the place. The book I'm...

Homework Statement If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on the sphere with center at the origin. Homework Equations I know dot product might help: r(t) . r'(t) = 0 and the equation of a...

Homework Statement Find the parametric form for the tangent line to the graph of y=2x2−5x+3 at x=2 is Homework Equations I have no clue! The Attempt at a Solution I found the tangent line to be y=3x-5 I know that the answer has to be in the form... <x0,y0>+t<x1-x0,y1-y0> I...

If the first derivative of a function represents the gradient of the tangent line... What does the second derivative represent? Thanks in advance James

Given is a curve \gamma from \mathbb{R} \rightarrow M for some manifold M. The tangent to \gamma at c is defined as (\gamma_*c)g = \frac{dg \circ {\gamma}}{du}(c) Now, the curve is to be reparameterized so that \tau = \gamma \circ f, with f defining the reparametrization. (f' > 0...

I am trying to do some calculations that involve cubic Bezier curves. I've been looking all over the place for information about Bezier curves, but I can't find anything that has what I'm looking for. I need to be able to figure out the length of any curve with known control points...

Say I have a curve is called C: y=1287*x^-1.5 Find a tangent line to the C, and the tangent line has to have a intercept of 150. This is not a homework, not at all.

Finding the Equation of Tangent line on cos wave! Find the equation of the normal line to y = 2cos ( 4x) at x = \pi / 3 I don't even know where to start with this question, i have searched the textbook and internet, help would be appreciated.

For a tangent plane to a surface, why is the normal vector for this plane equal to the gradient vector? Or is it not?

Hi, everyone: I am going over J.Lee's Smooth Manifolds, Chapter 3; specifically, Lemmas 3.1, 3.4, in which he states properties of derivations. Lee calls linear maps L with the Leibniz property (i.e L(fg)(a)=f(a)L(g)+g(a)L(f) ) derivations, when these maps are defined in a...

Homework Statement Show that the tangent to the ellipse ax^2+by^2=1 at the point (h,k) has equation ahx+bky=1 Hence, deduce that the chord of contact of tangents from the point (m,n) to the ellipse ax^2+by^2=1 has equation amx+bny=1 Homework Equations The Attempt at a Solution...

hi every one, i have one doubt i studied abt trignomentry. there finding the triangle angle or side of the triangle using sine function. if we are taking right angle triangle sine A = opp/hypo, cos A = adj/hypo and tan A=opp/adj. here we are finding angle for A only why we are having three...

Homework Statement See figure. Homework Equations The Attempt at a Solution Rearranging my equation, z = \sqrt{\frac{x^{3}+3y^{2}-3}{3}} Let f(x,y) = \sqrt{\frac{x^{3}+3y^{2}-3}{3}} Then, f_{x}(x,y) = \sqrt{x^{2}} f_{y}(x,y) = \sqrt{2y} So, f_{x}(3,1) = \pm...

I'm not sure I fully understand the difference between these two terms when used in differential geometry/general relativity. If I were to describe covariant differentiation to someone, I would say something like this: "On a curved manifold (imagine a basketball), you could assume a tangent...

Hi, I'm trying to get this working for a program I'm making. I've been working on this for a while, but I can't seem to figure it out. I have multiple rotated ellipses. Imagine you took a rubber band and stretched it around the ellipses. The rubber band would follow the curve of the outside...

Homework Statement Show that the curve γ(t)=(t²-t+1,t³-t) has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point. I have found the self intersection. I know that a unit tangent vector is the derivative of each...

Homework Statement Find the equation of the line that is perpendicular to the tangent line to the curve, y=(3x+1)/(4x-2) at the point (1,2) Homework Equations The Attempt at a Solution I am absolutely confused with this problem. I tried taking a derivative of the equation. And I...

Homework Statement ok so this is going to be divided into 2 parts, 1st is related to First Principle to obtain the derivative,the 2nd part is about obtaining equations of the tangent. I'd like to apologize for not being able to write the equations and my work neatly as other threads seem to...

Homework Statement See first figure. Homework Equations The Attempt at a Solution See second figure. When I set t = 0 in \vec{r(t)} I get 0\hat{i} +2\hat{j} + 1\hat{k}. I know this is a vector and not a point but it has the same "coordinates" as the point they are asking us...

Homework Statement Let P be any point (except the origin) on the curve r=f(θ). If ψ is the angle between the tangent line at P and the radial line OP, show that tan(ψ)= (r/(dr/dθ)) Hint: Observe that ψ = φ - θ in the figure. Homework Equations Very few equations come to mind except y =...

Hello Everyone, I'm doing my math in advance so I came across a Trigonometry question I came across in my textbook. I did make some progress but I do not know how to go about it further. Homework Statement Prove that, tan3A + tan2A + tanA = tan3Atan2AtanA The Attempt at a...

Homework Statement Find the equation of a tangent line at the curve at point (-3√3, 1) x^(1/3) + y^(1/3) = 4Homework Equations Point-slope: y-1=m(x-1) The Attempt at a Solution I took the derivative of that equation and resulted in -y^(2/3)/x^(2/3) When I tried plugging in x and y to...

Hello, Consider x \in (0,1) , that is x between 0 and 1. Can someone explain why the following is true: \frac{x-1}{x+1} = \tanh \left( \ln \left( \frac{x}{2} \right) \right)

A triangle ABC, where ,<A = 60 degrees. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E, and F be the points at which O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the circle O. (but AE line not cross...