Tangent Definition and 1000 Threads

Homework Statement Consider the following curve. y = 4 + 4x2 - 2x3. (a) Find the slope of the tangent to the curve at the point where x = a. Homework Equations m=y(a+h) - y(a)/h The Attempt at a Solution 1. m=y(a+h) - y(a)/h = -a^3-a^2+3ah+h^2-4 2. 6a^2 3. -6a^2+8a I know the derivative is...

Homework Statement the value of f(x) = (sqrrt e^x +3) at x=0.08 obtained from the tangent to the graph at x=0 is...? Homework Equations The Attempt at a Solution i used linear approximation. (sqrrt e^o +3) + (1/2(sqrrt3+e^0)(0.08) i got an answer but i know its wrong. i...

I am having a time trying to figure out this problem given only an x value. The equation is "Find the equation of the tangent line to y= Square root of x^4-2337 ...at x=7. If anybody could help me solve this it would be a great help. Thanks

I have a function: y=e^x the tangent line at the point (1,e) would be x*e? in order to find the area between the tangent line, the y-axis and y=e^x i equate these functions and solve for x? I got this far (e^x)/(x)=e how do i solve for x

Homework Statement Find an equation for the tangent to the curve at the given point. Then sketch the curve and tangent together Homework Equations y=3-x^2 (-1,2) The Attempt at a Solution slope = f(x + h) + f(x) / h f(-1 + h) + 2 / h 3- (-x + h)^2 + 2 / h 3 - 1 + 2h + H^2 + 2...

An Unknown Conic and Equation of Tangent Line **HELP** Homework Statement (a) Find the positive y-coordinate of the point on the conic whose x-coordinate is 27cos\theta, where 0<\theta<\pi/2 (b) The slope of the tangent line to the conic through the point (27cos\theta, y1) is -1/27cot\theta...

Homework Statement Problem: Find the equations of all tangent lines to the curve y = x + 2x so that also go through the point (3, 14). 2. Do not use a derivitive 3. I don't even know where to start. I searched my book there isn't really available. Any help would be much appreciated

The curve defined by x3 +xy - y2 = 10 has a vertical tangent line when x = ? To find when the tangent line is vertical, could I find when the slope is undefined for the original function? The way I previously tried this problem was by taking the first derivative and then finding when x = 0...

Homework Statement Given the function y = x^{2} + 3x - 4 find, a) the equation of tangent + normal at x = -2. b)the equation of the tangent that has slope of -2. c)local min and max. d)the equations of the tangent from the point (2 , -4) to the curve. e) area enclosed by the tangent at...

Homework Statement 4x - 2xy = 0 how do i solve for EITHER x or y? Homework Equations The Attempt at a Solution i got y = 2 at first but when i plugged it into the original equation to find x it was impossible to get an answer (the x's canceled out)

Hi In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as (i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)] in an introduction to second order PDEs I'm a bit confused by this. Where did it come from? Can anyone explain Thanks

Hi In my lecturer's notes he describes the unit tangent to a curve y=Y(X) as (i + Y'(X)j)/[(1+[Y'(X)]^2)^(0.5)] in an introduction to second order PDEs I'm a bit confused by this. Where did it come from? Can anyone explain Thanks

Hello, I'm trying (somewhat haphazardly) to teach myself about differential forms. A question I have which is confusing me at the moment is about the tangent and cotangent spaces. In https://www.physicsforums.com/showthread.php?t=2953" the basis for the tangent space was described in terms of...

Homework Statement Find the equation of the tangent line to the curve 3xy = x^3 + y^3 at point (2/3,4/3) Homework Equations The Attempt at a Solution I found the deriviative to be 3x^2-3y / 3x - 3y^2 which i simplified to x^2 - y / x - y^2 I found the slope of at those...

Homework Statement Find the slope(s) of the tangent at x = 1 for 2y^2 - xy -x^2 = 0 Homework Equations The Attempt at a Solution Ive figured the derivative to be 2x+4/4y+x But I don't know how to make this equation work to find a y value so I can find the slope. I tried...

I encountered a few problems for a few questions while doing my homework. 1. Angular measure problem: A Ferris wheel with a radius of 25.3m makes 2 rotations every minute. a) Find the average angular speed of the Ferris wheel in radians per second. b) How far does a rider travel if the ride...

Homework Statement Find the point on the graph y = sqrt 2x-1 where the tangent line is parallel to x - 3y = 16 Homework Equations The Attempt at a Solution So what I started off was was trying to find the slope of x - 3y = 16. I rearranged the equation to a y = equation and...

Homework Statement Let C be the intersection of the two surfaces: S1: x^2 + 4y^2 + z^2 = 6; s2: z = x^2 + 2y; Show that the point (1, -1, -1) is on the curve C and find the tangent line to the curve C at the point (1, -1, -1). Homework Equations partial derivates, maybe the gradient...

Homework Statement Find an equation for the line tangent to to the graph of f^-1 at the pt (3,1) if f(x)=x^3+2x^2-x+1 Homework Equations The Attempt at a Solution I used the Inverse Function Thm 1/(3x^2+4x) Now do I plug in 3 to this to find slope? 1/21 y-1=1/21(x-3)...

Homework Statement Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4 Homework Equations Not sure The Attempt at a Solution Not sure quite how to approach this. take the gradient of...

Homework Statement Find the equations of the tangent plane and the normal line to the given surface at the specified point. xy+yz+zx=3 @ (1,1,1) Homework Equations z-z0=fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) The Attempt at a Solution I feel like this should be really easy, but I'm...

Homework Statement Find the slope of the tangent to y=3x2 - 6x at x = 2 by first determining the derivative of the function from first principles Homework Equations f(x+h)-f(x) / h The Attempt at a Solution For the derivative I got -6x and the slope of the tangent is -12...

So we are given T(t) = c'(t)/||c'(t)|| as well as ||T|| = 1 We also know T(t)dotT(t) = 1 and T'(t)dotT(t) = 0 The problem asks us to find T'(t) I tried differentiating c'(t)/||c'(t)|| treating ||c'(t)|| as the square root of the dot product of c'(t) with itself. I used the product...

Homework Statement A surface is given by the equation 2x2+y2-z2=64 Find all points p on the surface where the tangent plane is parallel to the plane 12x+y-3z=0. Homework Equations I know the equation of a plane tangent to a surface at point (x0,y0,z0) is given by the equation...

Homework Statement Determine the points on the ellipse x^2 a 2y^2=1 where the tangent line has a slope of 1 Homework Equations I'm able to solve problems when given points and asked to find equations of the tangent lines. However, I'm struggling to do the inverse. The Attempt at a Solution...

Homework Statement Find an Equation of the tangent line to the curve y=10^x at the point (1,10) Homework Equations Derivative y=mx+b The Attempt at a Solution I am totally lost I don't know what to do with 10^x Please help me this will save me failing the class

I recently came across a problem where I was able to show that \sum_{n=1}^{\infty} \frac{(-1)^n}{n} \tanh \left( \frac{n \pi}{2} \right)=\frac{\ln 2- \pi}{4} through numerical approximation...However, I don't have much practice evaluating such summations analytically, and I was wondering if...

Homework Statement Find the equations of all the tangent lines to x^2 + 4y^2 = 36 that pass through the point (12,3) Homework Equations the derivative of the ellipse is dy/dx = -2x/8y (I'm not sure if that is correct, i have only recently learned implicit differentiation.) The...

Homework Statement r(t) = 〈sin(t) − t cos(t), cos(t) +t sin(t), 5 t2 + 7 〉 Find the unit tangent. T(t)= The Attempt at a Solution r'(t) = <cos(t) + tsin(t), -sin(t) + tcos(t), 10t> T(t) = r'(t)/ |r'(t)| |r(t)| = sqrt( 1 + 101t^2) And so on. Supposably according to the...

So I'm trying to learn about fibre bundles and I am looking at the example of a tangent bundle. Given a differentiable manifold M. Denote the tangent space at p \in M by T_p M. Is the definition of the tangent bundle TM = \lbrace (p, T_p M)|p \in M \rbrace or is it TM = \lbrace...

Hi i have a very basic question in calculus. i know that the tangent to the curve y=f(x) is denoted by dy/dx which makes sense to me geometrically. But normal to a surface k(x1,x2,x3) is Grad k. how is this? it doesn't make sense to me geometrically. can anyone throw more light upon this please

Homework Statement On the circles y^2+x^2=1 and y^2+(x-3)^2=4 There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle. Homework Equations the derivative of the first circle i found: y'=-x/y the derivative of...

How can I create a line tangent to a spline curve interpolated with several points in 2D in pro/engineer wildfire2.

Homework Statement The tangent line through given points (pi/4,pi/4) m=1 y= cos(y)cos(x)/sin(x)sin(y) The Attempt at a Solution dy/dx= d/dx[cos(y)cos(x)/sin(x)sin(y)] First use quotient rule ? vu'-uv'/v^2 v= sin(x)sin(y) v'= do i need to use product rule? for product rule...

Homework Statement Let (x0,y0) be a point on the graph f(x) = x2 for x0 not equal to 0. Find the equation of the line tangent to the graph of f at that point by finding a line that intersects the cure in exactly one point. Do not use the derivative to find this line.Homework Equations f(x) =...

Homework Statement For what values of a and b is the line 3x+y=b tangent to the curve y=ax^3 when x=5 ? The Attempt at a Solution I believe i would need to find the equation of the tangent to y=ax^3 when x=5 then that should be equal to -3x+b=y if I am not mistaken but I am not sure...

Let me first confess this a copy/paste of a question I asked on another forum; I trust it's not against the rules. Let M be a C^{\infty} manifold, and, for some neighbourhood U\ni p \subsetneq M let there be local coordinates x^i such that p=(x^1,\,x^2,...,x^n) Suppose that T_pM is a...

Homework Statement r(t) = costi + 2 sint j Find the tangent vector r'(t) and the corresponding unit tangent vector u(t) at point P:(.5, 3.5,0) Homework Equations r'(t) = r(t)dt u(t) = r'(t) / |r'(t)| The Attempt at a Solution r'(t) = -sinti + 2costj |r'(t)| = [sin2t +...

Just when I thought I got the hang of tangent planes and surfaces there comes a question I haven't quite seen before z = ln (x^{2}+3y^{2}) Find a normal vector n and the equation of the tangent plane to the surface at the point (2, -1, ln 7) So keeping the cartesian equation in mind: z =...

Homework Statement x = e^{t} , y = (t-1)^{2} , (1,1) Find an equation of the tangent to the curve at a given point by two methods. Without eliminating the parameter and by first eliminating the parameter. The answer in the book says y = -2x + 3 and I cannot see how you get it. So...

Suppose that F(x,y) = x^{2}+y^{2}. By using vector geometry, find the Cartesian equation of the tangent plan to the surface z = F(x,y) at the point where (x,y,z) = (1,2,5). Find also a vector n that is normal to the surface at this point...

Okay, so I am supposed to expand ln(cos(x)) basing my calculations on tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ... and expanding out to that fourth term is sufficient. I am having a major brain meltdown, I can't seem to find any equivalencies present, and I'm sure there are. Any help...

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 a sphere with center at the origin Homework Equations The Attempt at a Solution I have no idea how to even approach this...

Homework Statement Find the slope of the tangent line to the curve y=x3 at point (-1,-1) (i) Using Definition 1 m=limx-->a\frac{f(x)-f(a)}{x-a} (i) Using Equation 2 m=limh-->0\frac{f(a+h)-f(a)}{h} Homework Equations The Attempt at a Solution For the first one, I got as far...

Homework Statement Ok, how do i solve this question I've attached the picture.. The answer is A but i don't understand how to get that... The Attempt at a Solution The solution is also given , but i don't understand the adding and subtracting 5. the Derivative of y=ln (e^x + 5) y'=...

Homework Statement Find the area of the region bounded by the graph of f(x) = 4x^2, the tangent line to this graph at P(2, f(2)), and the x-axis Homework Equations Integral of [f(x)-g(x) dx] The Attempt at a Solution I first tried to find the equation for the tangent line The...

Homework Statement f(x) = 4x-x2 Question: Find the equations of the lines that pass through P(2,7) and are tangent to the graph of f(x). (P is not on f(x).) Thats all the problem states. Homework Equations f(x) = 4x-x2 Point (2,7) The Attempt at a Solution Ive tried...

In order to find the equation of a line that is tangent to f(x) and goes through point P on f, you got to find the derivative of f(x) at P, but how would you go about solving a problem where you have to find the equation of a line tangent to f(x) that goes through point P, but P is NOT on the...

EDIT: Ugh... I meant "calculating", of course. This is an assignment that was due on the 16th. It's already been handed in, I just need some help with a question that I obviously was not able to answer in due time. I am coming back from a long, long hiatus from my academic pursuits and so some...

Homework Statement A ball that is circling with x=cos(2t), y=sin(2t) flies off on a tangent at t=Pi/8. find its departure point and its position vector at a later time t (linear motion; compute its constant velocity v). Homework Equations v=dR/dt T=v/|v|= (dR/dt)/(ds/dt)=dR/ds...