(a) Given that the transition curve of the highway is modelled after the curve y=4sin x-sin 2 x. Determine the curvature of the curve at x=- 2

Q: 1. Calculate the moment of inertia about x-axis of the first quadrant portion of the curve: y = 4-…

A:

Q: 4. Find the curvature * 5 K of the curve ř (1) = (e' cos(t), e' sin(t), 3) at t = 0.

A: Given data: The given expression for the curve is r→(t)=et cost, et sint,3. The given point is t=0.…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Consider the given parametric equations, xt=tyt=e-4tzt=5t-t5 Here we need to find the parametric…

Q: 3) Find the radius of curvature for the parametric curve e-t cost , y = e-t sin t.

A: Given parametric curve is x=e-tcost, y=e-tsint. We know that the Radius of curvature of a parametric…

Q: 3. Find the curvature of the curve given by 7(t) = (t, t², t) nt (-1, 1, –1).

A: Given curve is We know that curvature to given curve at point (-1,1,-1) , that is at t=-1 is

Q: . Find an equation for the circle of curvature of the curver(t) = ti + (sin t)j at the point (pi/2,…

A: The parameterized curve are x = t , y = sin t The derivatives are                           y = sin…

Q: -*) at (0, 1). Find the center of curvature of the curve

A:

Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Find the curvature of the curve defined by F (+) = (5 cos(t), 6 sin(t)) at t = 2

A: κ=  r'(t)→× r"(t)→r'(t)→3 We have to just evaluate for given r(t)

Q: Find the curvature of the curve defined by 7(t) = (6 cos(t), 3 sin(t)) at t 6

A:

Q: 4) Find the curvature of y = cos x at the point (÷,²). Then find the equation of the osculating…

A:

Q: 8. Find the curvature of the plain curve y = e.

A: According to our guidelines, we can answer only one question. Other questions can be reposted.

Q: 3) Find the radius of curvature for the parametric curve e-t cost, y = e-t sin t.

A:

Q: 3. Find the radius of curvature at any point of the curve y = a Cosh ( x/a)

A: solution:-  The given curve is  .y=a coshxa.........eqo1

Q: Calculate the curvature and radius of curvature of the graph of the function y=√x at x=1

A:

Q: Find an equation for the circle of curvature of the curve r(t) = 8ti +sin(5t)j  at the point (4pi,…

A: Consider the parametrized curve y = sin ((5/8)x). its derivative can be found as follows.

Q: What is the equation for curvature for the curvey=sin(x)? What is the curvature of the curve…

A: The equation of the circle of curvature is calculated using the formula: x-x2+y-y2=ρ2, where:…

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j+k.

A:

Q: 3. Find the curvature of f(x) = e" at point (0, 1). Then find the equation of the osculating circle…

A:

Q: at a unit-speed regular parametrised curve 3: (-7, 7)→ R² with T, N) has constant curvature k> 0.…

A: Sol

Q: Q2 Find the radius of curvature of yv5 = x' at the point (x, y,). Hence, show that the radius of…

A: Use formula of radius of curvature

Q: At what point does the curve have maximum curvature? y = 9 ln(x)

A:

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

A:

Q: Find the curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

Q: find the curvature at typical point (x,y) on the curve y=x²

A:

Q: 4. Find the radius and centre of curvature of the curve x = (1 - at) cos t + a sin t, y = (1 – at)…

A:

Q: Find the curvature and radius of curvature of the plane curve y = tan x at the given value of x == π…

A: To find the curvature and radius of curvature of the plane curve y=tanx at x=π4.

Q: Find the curvature and the radius of curvature at any point on the curve y = In sec x.

A: A curve given y = ln (secx)  Find out the curvature and the radius of the curvature of given curve.

Q: Consider the curve given by the equation y2+x3=0. Find its curvature at the point (−1,1).

A:

Q: 1 at the point (1,1). Find the curvature of the curve f (x) =

A: We need to find the curvature of the curve fx=1x at the point 1,1.

Q: At what point does the curve have maximum curvature? y = 9 ln(x) (x,y) =? what happens to the…

A: we are given we can use formula now, we can plug it and we get

Q: Find the curvature of he curve :  at x^2/3 at x=1

A: GivenLet f(x)=x23To find the curvature of the given curveFormula:ρ=1+f'(x)232f''(x)

Q: The curvature of a point moving along the curve given as R(t)=(ln sec t) i+ tj is

A:

Q: 1. Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point (7.5.0).

A: First partially differentiate the function with respect to x,y and z and then proceed as shown…

Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: 7) Find the curvature of y = e* at the point (0, 1). Then find the equation of the osculating circle…

A: Given curve, y=ex

Q: 3) Find the radius of curvature for the parametric curve x = e-t cost , y = e-t sin t.

A:

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A:

Q: Find an equation for the circle of curvature of the curve r(t) = ti + (sint)j at the point ('pi/2,…

A: Givenr(t)=t i+(sint) j,       y=sinx,     point=π2,1We have to calculate equation for circle of…

Q: 2. Find the curvature of the curve x(t) t = 1. %3D at

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the curvature and radius of curvature of the plane curve y = ln x , at the given value of x =…

A: The Curvature of the curve y= f(x) and the radius of curvature of the curve at the point is…

Q: Determine the curvature of the curve y=arctanx at x=0 and at infinity.

A:

Q: Compute the curvature of the curve y=x^2+4x+1 at the point on the curve when x=1.  Give the exact…

A: Given, y= x²+4x+1 x=1

Q: 2) Find and sketch the circle of curvature at the point on the curve y x where the tangent line has…

A:

Q: At what point does the curve have maximum curvature? y = 7 In(x) (x, y) = What happens to the…

A: Given,              y = 7 ln(x)

Q: Find an equation for the circle of curvature of the curve r(t) = t i + (sin t)j at the point (pai/2,…

A: The parameterized curve are x = t, y = sin t.The derivatives are,