Tangent Definition and 1000 Threads

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

Homework Statement Solve: 2 tan x (tan x - 1) = 3. Homework Equations Pythagorean identities? The Attempt at a Solution I tried the following: 2 tan^2 x - 2 tan x = 3 2 (sec^2 x - 1) - 2 tan x = 3 2 (1 - cos^2 x) - 2 sin x cos x = 3 cos^2 x (multiplying through by cos^2 x)...

I'm having some difficulty with this problem and any help would be appreciated. What is the radius of a circle tangent to the lines y = 3x + 7 and y = .5x - 3 and containing the point (8,1)? I've determined that the given point (8,1) is the point of tangency of the line y = .5x - 3 and the...

Hi Appologies for formatting issues this is the first time I have submitted something to the forum. I have a pretty simple problem, I am just going through the derivation of the First Fundamental Form and I think I am missing something in the derivation. If we have a point x = (x1,x2)...

Do we have identities for the following $$\arctan(x+y) = $$ $$\arctan(x)-\arctan(y) = $$

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

What is meant by the tangent weight of a spline?

Why does tangent go to infinity when it increases 0 to 90 degrees?

Homework Statement Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4)) Homework Equations The Attempt at a Solution f'(x)= e^(2x) * (2x+ 1) (e^4)(5) = 5e^4 y- 2*e^4 = 5*e^4 (x-2) y= 5(e^4)*x - 8*(e^4) Is this right? It seems too easy...

Homework Statement Find the points on the graph of x3-y3=3xy-3 where the tangent line is horizontal Homework Equations y = f(x) so implicit differentiation must be used when taking the derivative of y (xy)' = xy' + y The Attempt at a Solution So if the tangent line is...

Homework Statement Determine a line that is tangent to both f(x)=x2 and g(x)=x2-2x Homework Equations The Attempt at a Solution f(x)=x2 => f'(x)=2x g(x)=x2-2x => g'(x)=2x-2 f'(a) = f'(b) 2a = 2b-2 I don't know how to continue. Thanks for help.

Homework Statement Give the equation of the line tangent to the curve at the given point. ytan^-1x = xy at (sqrt3,0) Homework Equations The Attempt at a Solution Would it be right to do an implicit differentiation or to isolate for y here? I isolated for y and got...

Homework Statement Find an equation of the tangent line at the point indicated f(x) = 5x2-2x+9 , x = 1 Homework Equations (d/dx) bx = ln(b)bx General Power Rule which states: (d/dx) g(x)n = n(g(x))n-1 * g'(x) The Attempt at a Solution So looking at a previous problem...

Hello MHB, I got one question, I am currently working with an old exam and I am suposed to draw it with vertican/horizontal lines (and those that are oblique). $$f(x)=\frac{x}{2}+\tan^{-1}(\frac{1}{x})$$ for the horizontel line $$\lim_{x->\infty^{\pm}}\frac{x}{2}+\tan^{-1}(\frac{x}{2})$$ Is it...

Here are the questions: Here is a link to the questions: Equation of tangent and normal? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hello MHB, I am doing some old exam and got less knowledge for this problem. consider the graph of the function $$g(x)=\frac{1}{x}, \ x\neq 0$$ the point $$\left(3,-1 \right)$$ lies on two tangents to the graph. Decide tangents equation. My progress well I derivate and find the slope...

Here is the question: Here is a link to the question: Finding tangent line with definite integral? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Given that the curve y = x^3 has a tangent line that passes through point (0, 2), find the area of the region enclosed by the curve and the line by the following steps. Homework Equations The Attempt at a Solution Let f(x) = x^3 and let the coordinates of the...

Homework Statement The line x-2y+9=0 is tangent to the graph of y=f(x) at (3,6) and is also parallel to the line through (1,f(1)) and (5,f(5)). If f is differentiable on the closed interval [1,5] and f(1)=2, find f(5) A) 2 B) 3 C) 4 D) 5 E) None of these The correct answer is (C) 4The Attempt...

Lets imagine a binary system of two astronauts in space connected to one another via light rope. The rope is taut and they're spinning round and round with their axis of rotation being the the axis perpendicular to the their centre of mass. Now, my question is this. Let's say they each let go...

Homework Statement If f(x,y) = xy, find the gradient vector \nabla f(3,2) and use it to find the tangent line to the level curve f(x,y) = 6 at the point (3,2) Homework Equations The Attempt at a Solution f(x,y)=xy \Rightarrow\nabla f(x,y)=<y,x>,\nabla f(3,2)=<2,3> \nabla...

I am currently working with parametric equation and trying to solve finding points on the curve where the tangent is horizontal or vertical. When I do with trigometry I get problem... And I need help to understand this. I know what vertical and horizontal means. exemple this one i am working...

Okay, so I am in grade 12 calc and I was learning about e today, how the slope of the tangent at any point is also the y value at that point. What I was wondering is if there is a function that has the x value equal to the slope at any given point. I think it would look something like a...

If we have a manifold with a chart projected onto ##R^n## cartesian space and define a curve ##f(x^\mu(\lambda))=g(\lambda)## then we can write the identity \frac{dg}{d\lambda} = \frac{dx^\mu}{d\lambda} \frac{\partial f}{\partial x^\mu} in the operator form: \frac{d}{d\lambda} =...

Homework Statement Consider a surface ω with equation: x^2 + y^2 + 4z^2 = 16 Find an equation for the tangent plane to ω at point (a,b,c). Homework Equations Tangent plane, 3 variables: f_{1}(a,b,c)(x-a) + f_{2}(a,b,c)(y-b) + f_{3}(a,b,c)(z-c)= 0 The Attempt at a Solution I get at the...

Hello MHB, Find and an equation of the tangent(s) to the curve at the given point $$x=2\sin(2t)$$, $$y=2\sin(t)$$ $$\left(\sqrt{3},1 \right)$$ first we need to find the slope so we derivate $$\frac{dy}{dt}=2\cos(t)$$, $$\frac{dx}{dt}=4\cos(2t)$$ so we got $$\frac{dy}{dx}=...

1+50sinx/x^2+3 -5 < x < 5 3 zeroes: 0.02, 3.16, -3.12 Find the derivative and the slopes of the tangent lines. I need help with the last part. I found out the three zeroes by adding and subtracting pi from the equation at top by setting it to zero. Thank you!

The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: $$d/2.$$

Homework Statement find the points on the surface x^2 + y^2 + z^2 = 7 where its tangent plane is parallel to 2x + 4y + 6z = 1 Homework Equations Equation of a tangent plane: fx(x - x0) + fy(y - y0) + fz(z - z0) = 0, where fx means partial derivative of f respect to x n1 X n2 = 0 The Attempt...

Homework Statement Tangent to C at point P(2,7) has an equation of y=3x+1. Point Q also lies on C and is perpendicular to the tangent, show that the X-coordinate is [1/3(2+√6)] Homework Equations curve C has equation y= x3-2x2-x+9 dy/dx = 3x2-4x-1 The Attempt at a Solution gradient of...

Homework Statement 7 Find the points on the ellipse x^2 + 2y^2 = 1 where the tangent line has slope 1 Homework Equations The Attempt at a Solution I got the correct X and Y values but this gives me four possibilities and the answer key says there are two points. I got x...

1. Given. F(x) = 4x/(x^2+1) 2. Problem Find all points (x,y) where the function has a horiztonal tangent line 3. Attempt I took the derivative of F(x) and came to (-4x^2+4)/(x^2+1)^2 I set it equal to zero and found an x value of 1. I used that x value and plugged it into...

Hi everyone, I've been looking for the finite sum formulae of trig functions. I've found the easiest ones (sine and cosine). But the one for the tangent seems to be very hard. No mathematical tricks work. Plus I've looked it up on the internet. Nothing. I will greatly appreciate your help...

Homework Statement The equation of the tangent to the curve f(x)=ax^3+bx at the point of contact (-1;3) is y-x-4=0. Calculate the values of a and b Homework Equations y-y1=m(x-x1) The Attempt at a Solution I am totally stuck, here is what I could derive: Equation of tangent...

Here is the question: Here is a link to the question: Pre-calc math problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement At what points on the curve y = (x^2)/(2x+5) is the tangent line horizontal? Homework Equations Quotient rule The Attempt at a Solution I figured out the derivative which is 2x(2x+5) - 2x^2 ----------------- (2x+5)^2 I also know that for the equation of...

Hello, I got problem with A homework "find an equation of the tangent line to curve at the given point. $y=sec(x)$. $(pi/3,2)$ progress: $y'=sec(x)tan(x)$. So basicly that sec(x) don't say me much so i rewrite it as $1/cos(x)$ $y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to...

So let ℝ^{n}_{a}={(a,v) : a \in ℝ^{n}, v \in ℝ^{n}} so any geometric tangent vector, which is an element of ℝ^{n}_{a} yields a map Dv|af = Dvf(a) = \frac{d}{dt}|_{t=0}f(a+tv) this operation is linear over ℝ and satisfies the product rule Dv|a(fg) = f(a)Dvg + g(a)Dvf if v|a =...

Homework Statement If M and N are smooth manifolds, then T(MxN) is diffeomorphic to TM x TN Homework Equations The Attempt at a Solution So I'm here let ((p,q),v) \in T(MxN) then p \in M and q \in N and v \in T(p,q)(MxN). so T(p,q)(MxN) v = \sum_{i=1}^{m+n}...

Here is the question: Here is a link to the question: An equation of the tangent line to the curve y=f(x)=x(10cos x- 2sinx) at the point (4pi, f(4pi)) is y=? - Yahoo! Answers I have posted a link there to this topic, so the OP can find my response.

"find a unit tangent vector and the equation of the tangent line to the curve r(t) = (t, t^2, cost), t>=0 at the point r(pi/2)." NOW, what I don't get is, how is that a curve? This is not like the example I have studied and I don't really get the question. So I don't know where to start. Once I...

Homework Statement Find the number of tangent lines to the curve: y=\frac{3x}{x-2} which pass through the point (-1,9). Find also the points of contact of these tangent lines with the curve.The Attempt at a Solution 1. I found the equation of lines passing through (-1,9) -> y=(x+1)m+9 2. I...

1. Find the values for x at which the tangent line is horizontal 2. f(x) = x + 2sinx 3. I found the derivative to be f'(x) = 1 + 2cosx I then set the derivative equal to zero and it came out to be 2cosx = -1, cosx = -\frac{1}{2} So the values of the horizontal tangent are 2∏/3 ± 2∏

Homework Statement I have a surface given by z=x^2 - y^2 and its tangent plane at the point (x,y)=(1,1) given by z = 2x-2y. I am asked to compute the intersection of the tangent plane with the surface. The Attempt at a Solution I did the obvious and set x^2-y^2 = 2x -2y to find the x,y...

Homework Statement Show that, for each real number t \in the interval (0, 1], the curve given by: y=ln(\frac{x+\sqrt{1+x^{2}}}{1+\sqrt{2}}) has a tangent line with slope t. Find the points on the curve at which the tangent line has slope 2/3. The Attempt at a Solution I found the first...

An ellipse has the equation x^2+5y^2=5 a line has the equation y=mx+c a) show that if the line is a tangent to the ellipse then c^2=5m^2+1 b) hence find the equation of the tangent parallel to the line x-2y+1=0 I tried to find the gradient of x^2+5y^2=5 at a point (x1,y1) and then put it...

Hi, I recently learned that to find the tangent at a point on any curve, you can simply place a mirror on that point and reflect the part of the curve on one side of that point such that the reflection flows smoothly into the other part of the curve on the other side. Once this is done, draw a...

\Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\omega t+\delta)}\right) I want to find out whether ##\Psi## increase or decrease with time t, if ##\delta## is positive and if ##\delta## is negative. \Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\cos\omega t \cos \delta+\sin\omega t...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Homework Equations x = t \\ y = e^{-4t} \\ z = 5t - t^5 \\ P = (0, 1, 0) The Attempt at a Solution \vec{r}(t) = < t, e^{-4t}, 5t - t^5 > At the point...

Homework Statement Given the two parabolas: f(x) = x^2 - 2x + 2 and g(x) = -x^2 - 2x - 2. Find the equation of a line that is tangent to both curves.Homework Equations The given parabolas, equation for a line y = mx + b, and the derivatives of the two parabolas 2x - 2 and -2x - 2 The...