Find the curvature K of r(t)= 2ti +t²j - k 3

Q: Find the curvature of r(t) = at t = ,.

A: Given: r→t=3cost, 3sint, t Calculation: Compute the Curvature at t=π2 as follows. It is known that…

Q: Find the curvature of r(t) = (In t, 2t, t²) at (0, 2, 1).

A: Given r(t) = <ln t, 2t, t2> To find the curvature (k) at (0, 2,1)

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: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let, is a regular parameterization of a curve. To show the curvature at  is .

Q: find the curvature of r(t)=⟨3t2, ln(t), t ln(t)⟩ at the point (3, 0, 0).

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Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: Find the radius of curvature at origin at (0,0) y - x = x2 + 2xy + y2

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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: Determine the maximum curvature for the graph of f(x) = 6 In (3x). The maximum curvature is at x =

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Q: Find the curvature when r(t)=  6t i + 1/2t2 j +t2 k

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Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

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

Q: Find the curvature of the curve C: r (t) = (e, e', 2t) at t = 0

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Q: Find the curvature of r(t)=[e*,e2",e 3t] at t=0.

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x - 32 ,…

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Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

A: Given function is rt=3cost ax+4sint ay+ t az To find curvature and radius of curvature

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: Find the curvature of the curve r(t) = eti + 4tj at the point P (1, 0) .

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Q: Exercise 3.2.10. Using K = (In - m²)/(EG – F²), show that the Gauss curvature of the R- sphere S²(R)…

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Q: 21. r(t) = t³ j + t² k %3D

A: Given  r(t)=t3j+t2k

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,…

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Q: Let the the position vecor be R(t) = (-t,2 cos(2t),2 sin(2t)). Compute the curvature x(t).

A: The position vector Rt=-t,2cos2t,2sin2t. We have curvature k(t).

Q: The curvature of y=x? is: None .a 1 (1+4x)/2 .b O (1-4x2)2 .cO -1 (1+4x)2 .d o «17 jo 4 Jiull uo…

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay +…

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Q: Use this theorem to find the curvature. r(t) = 2ti + 5 sin(t)j + 5 cos(t) k K(t)

A: →dcos(t)dt = -sin(t)→dsin(t)dt = cos(t)→ If, r→=a i + b j + c k    Then,  r→ = a2 + b2 + c2

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

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Q: b.) show that brnormal of the muolute the unit *-ズ+(c-s)で g =dG) |k-s) K| K* where K is the…

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Q: Use Theorem 11.24 to prove that the curvature of a linearfunction y = mx + b is zero for every value…

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Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

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Q: Find the curvature of the curve r(t) = (3 + t, – 4+ 2t, – 2 – t) at the point t = - 8.

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Q: FInd the curvature of f(t)=ti+t^2j+t^3k at (2,4,8)

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Q: Find the curvature of r(t) = √√7ti + etj + e-k at point P(0, 1, 1).

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Q: 1. Find the points on the parabola y 8x at which the radius of 125 curvature is 16

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Q: Find the center of curvature of the curve y=Inx at (1, 0). A) (4, 3) (в) (3,4) c) (3, -2) D (-2, 3)

A: Ans D

Q: Find the curvature K(t). r(t) = (4t, 3t, 2) %3D

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Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let,  is a regular parameterization of a curve To show the curvature at  is

Q: Find the curvature of the cardioid r=a(1+cosθ) at θ=0.

A: Given equation of cardioid is Derivatives of polar curve are

Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 6ti – 8tj, t = 1…

A: The formula for the curvature is κ(t) = r't×r''tr't3

Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 4ti – 6tj, t = 1…

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Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: 3. Find the moving trihedral and the curvature at any point of R(t) = (In(sect), t/V2,t/V2). %3D

A: Introduction: In differential geometry, the Frenet–Serret formulas define the kinematic properties…

Q: Find the curvature of r(t) = (t, 5, t²): at a general point, and at (1,5,1).

A: Given r→t=t,5,t2 and point is 1,5,1. We have to find the curvature of r→t=t,5,t2 at point 1,5,1 The…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

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

Q: 10.) At what point does the curve have maximum Curvature? y=In(x). K(x)= f"|

A: firstly find f, f' and f'' . And substitute all these values in given curvature formula.  After that…

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: Determine the maximum curvature for the graph of f(x) = 9 In (8x). The maximum curvature is at x=

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Q: Find the curvature K and the radius of curvature R at (1,2). (A K= √/2. R=₁ R = √2 (В) K= R= 2√2 2√2…

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Q: Find the curvature K for the space curve r(t) = (/3sint)i + (sint)j+ (2cost)k.

A: Let, γ(t) be a space curve. The curvature of the space curve is given by, κ=γ'(t)×γ"(t)γ'(t)3.

Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: x= 0, x= π &x= π

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

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Q: Determine the maximum curvature for the graph of f(x) = 7 In (2x). The maximum curvature is at x=

A: We are given function f(x)=7ln(2x) of the graph Formula for curvature is κ(x)=|f′′(x)(1+(f′(x))2)32|…

Q: Find the curvature of the space curve. r(t) = (6t sin t+ 6 cos t)i + 6j + (6t cos t-6 sin t)k 1 O A.…

A: Given space curve

Q: Find the gaussian and mean curvature functions of the surface m given by the equation y3=y1y2 in R³…

A: First parameterized the equation.

Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

A: