8. Find a plane curve a(s) endowed with a unit-speed prametrization by S E (-∞, 0) such that its signed curvature is equal to sin s.

Q: Find the curvature of y = sin(3T) at a = =.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 04. Show that the Gauas and mean curvatures on, X-(u+v,u-v, uv) at u=1, v=1 are K=1/16 and H= JI.…

A: Given: 1) X=(u+v,u-v,uv) at u=1,v=1. 2) The paraboloid is xy=aZ.

Q: Find the curvature of the plane curve Y = 4t* at the point t = 1. K(1) =

A: que: Curvature of a plane curve y = f(x) is given by K = y||(x)|(1+(y1(x))2)32 Here y = 4t4

Q: Find the curvature and radius of curvature of the plane curve at the given value of x . y = x −4/ x,…

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 the curvature and radius of curvature of the plane curve at the given value of x. y = xn, x =…

A: Given ,

Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: What is the curvature of the path of the motion at t=1

A: Since velocity is given we need to calculate  r''(t) only at t=1

Q: 7. Find the radius of curvature of the curve y = In sin x at x= r/2 .

A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

Q: 2.Let a be a unit speed curve lying on a sphere center c and radius a > 0. Find the minimum value of…

A: Given That : Let α be the unit speed  curve lying on a sphere center c and radius a>0. To Find :…

Q: Find the curvature of y = sin(3x) at a = 프 4

A: We Know that The curvature measures how fast a curve is changing direction at a given point.

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: Obtain the curvature of x= k (0 – sin 0); y=k(1+ cos0) in terms of '0'.

A: This is the question from application of advanced Differential Calculus.

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: 2 - Find the curvature of the curve at the point (1, 0, 0). r(t) (e' cos(t), et sen(t), t) %3D

A:

Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

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

A:

Q: Find the center of curvature of the curve y =-(e*+e) at (0, 1). (А) (0, 2) в) (1, 1) с) (0, 3) D (0,…

A:

Q: Q2 Find the radius of curvature of y5 =x at the point (x,v.). Hence, show that the radius of %3D…

A: The curve is y5=x3

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

A: Sol

Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: 2. Find the radius of curvature for the curve r*cos20 %3D 1.

A:

Q: |x'y" -y': y'a - y'= es K(t) = (x2 + у'?

A:

Q: 2-Show that the regular curve a = a(s) is a straight line if and only if its curvature k is…

A: Here we have to show that a regular curve is a straight line if and only if, its curvature is…

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Find the…

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = sin 2x, x…

A: Consider the provided equation, y=sin2x,   x=π4 Find the curvature and radius of curvature of the…

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

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: At what point does the curve y = e have maximum curvature? What happens to the curvature as x → ∞?

A:

Q: 15. y= 2x +3 at x = 27

A:

Q: 6. Consider the same curve from the last problem, C parametrized by T(t) = (2 cos t, –1,2 sin t)…

A:

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x3, x = 2

A: Consider the following equation of curve: y=x3 Differentiate y with respect to x: dydx=ddxx3y'=3x2…

Q: Find the curvature of the parabola f(x)= ax +bx+c at its vertex 2a ’

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: 15. Show that the ellipse x = acos t, y = b sin t, a > b> 0, has its largest curvature on its maior…

A: If a curve is defined in parametric form by x(t), y(t), then, the curvature at point M(x, y) is…

Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

A: The curvature of the curve αs is given by: αs=∫s0scos(θ(u))du, ∫s0ssin(θ(u))du-----(1) in which…

Q: 8. Find the curvature of the curve with parametric equation y = t³ –t and x = t? – 2t at t= 2.

A: Given parametric equations : y=t3-tx=t2-2t To find the curvature at t=2 The curvature is given by  :…

Q: Show that for a plane curve the torsion T = 0.

A: We have to shown that, For a plane curve the torsion T=0

Q: .3 Find the radius of curvature of y=x' at x=1,

A:

Q: Find the curvature K of the plane curve y 3 at x = 3. 2х + K =

A:

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: 4. Find the curvature of r(t) = (tv2, e', e-t) at the point (0,1,1).

A:

Q: Determine the radius of the curvature of the plane curve given by y In sec x at the || point (0,0).

A:

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: Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

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)