Use this theorem to find the curvature. r(t) = 9t i + 2 sin(t) j + 2 cos(t) k

Q: Find the curvature for the helix r(t) = (4cost)i +(4sin t) j +(3t)k

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Q: Use this theorem to find the curvature. r(t) = 7ti + 5sin(t)j + 5 cos(t) k

A: Consider the provided vector valued function, rt=7ti+5sintj+5costk Using the above theorem find the…

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

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

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Q: Find the curvature and radius of curvature of the parabola y=x² at the origin. O K= 2, p=1/2 O k=2x,…

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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: TU? TU? r(t) = (/ * du, sin -du ) , t > 0 COS 2 2

A: r(t)=∫0tcosπu22du,∫0tsinπu22du,t>0 We have to find the unit tangent vector T and Curvature K for…

Q: (b) Given that r(1)=(r.r.) Find the curvature of r(t) at the point P(2,4,2).

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Q: Find the curvature of the space curve. r(t) = -10 i + (t + 4) j +(In(cos t) +9) k %3D OK= sect K =…

A: Formula of radius of curvature:      k=r→'(t)×r→''(t)r→'(t)3 First we need to find r→'(t),r→''(t),…

Q: Calculate the curvature function κ(t). r(t) =〈4t + 1, 4t − 3, 2t〉

A: Given: r(t)=4t+1,4t-3,2t Differentiate the function. r'(t)=ddt4t+1,4t-3,2t=4,4,2 Again…

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

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Q: Given the vector function *(t) = (t, cos (2t)) Calculate the curvature when t=5.4

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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: a) Find a plane curve whose signed curvature is given by k,(s) where a is a positive constant and s>…

A: The given signed curvature is ks(s)=12as

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

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Q: Find the curvature of the space curve. r (1) = -8i + (1 + 4) j + (8 + In(cos t)) k %3D OK = sec t…

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Q: Consider the helix r(t)=(cos(3t),sin(3t),−1t). Compute, at t=π/6:  A.The unit tangent vector T= (…

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Q: Tuán:- Given the function R(+) = ( + -cos) i² + (sinds +3K, use the directed - product for mula to…

A: Given- Rt=t-costi→+sintj→+3k→ To calculate curvature at t=5 using directed product formula. The…

Q: 21. r(t) = t³ j + t² k %3D

A: Given  r(t)=t3j+t2k

Q: Find the curvature for a circle of radius a > 0, centered at the origin, and traced cut by the…

A: Explained below

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

A: Given y =e^(-x/4)  ,x=8 Now we have to find curvature and radius of curvature at x=8

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i+11…

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Q: 5. Given r = F(0), prove that the curvature is given by dr p2 + 2 do () dr - r de? K = 3 2 dr () p2…

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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: 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: 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: Find the curvature for the following vector function. 1. r(t)=( 4t, -t², 2t³)

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Q: Find the curvature of the given curve r(t) = 5ti +3sin(t)j + 3cos(t)k a. 2//34 b. 4//34 C. 3/34 d.…

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

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Q: laxv to find the curvature of the following parameterized curve. Use the alternative curvature…

A: Given: And Here, v = r'(t) and a = r''(t). So,  by using the above formula and r(t) we will now…

Q: 2. Let a(t) = (3t-t, 3t2, 3t + t), for te R. %3D (i) Calculate the equation of the osculating plane…

A: Introduction: The formula of curvature of and torsion is given by, κ(t)=α"(t)…

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: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Determine the curvature of r(t) = t^2 i+ t k

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

Q: Given r(t) = 2e"i+(2e² cost) ost)j+(2e* sint)k . Evaluate T(1), N(1), binormal vector, B(t), and the…

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Q: |r'(t) × r"(t)|| ||r'(t)||* Use the formula k(t) to find the curvature of the space curve at t = 0.…

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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: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: Consider the given equation of circle, γt=sint,cost,1 The formula for normal curvature is defined…

Q: Consider the helix r(t)=(cos(2t),sin(2t),−4t)r(t)=(cos⁡(2t),sin⁡(2t),−4t). Compute, at t=π6t: A.…

A: Given r(t)=cos2t , sin 2t   , -4t      ; t=π6

Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: Find the curvature of r(t) at the point (1, 1, 1). r(t) = (t, t², t³) k=

A: Given: vector valued function r(t)=<t, t2, t3>To Find: curvature at t=1

Q: Given x = t, y = 1/t, find the curvature at t = 2. 16 17√/17 O 16 17 O 16/17 17 16 √17

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Q: Find the curvature of r(t) = (2t, t²,-t³) as a function of the parameter t. Simplify your answer to…

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Q: Find the curvature of the plane curve. 13. r(t) =t² i+ j t = 2 14. r(t)=(t, sint) at t =- 2

A: 1)