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

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

A: Given that: The equation is y = e-x4 and the point x = 8 .

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: 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: 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: Find the curvature of the curve r(t) = (3 cos(t), 3 sin(t), 4t) at the point t Give your answer to…

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Q: Calculate the curvature of the position vector ř(t) = sin t āx + 2cos tāy + V3 sin tāz is a circle,…

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Q: Find the curvature of the curve r(t) = 4ti + 3 cos tj + 3 sin tk .

A: curve r(t) = 4ti + 3 cos tj + 3 sin tk . We need to find the curvature of the given curve.

Q: 1) Calculate the curvature of the position vector r(t) = sin tāx + 2costāy + V3 sin tāz is a circle,…

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

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Q: Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) = (4…

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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.

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

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Q: 3) Find the radius of curvature for the parametric X = сurve e-t cos t , y = e=t sin t.

A: R=1+dydx232d2ydx2 Given equations of curve- xt=e-tcostyt=e-tsint

Q: Find the curvature of the curve defined by F(t) = (6 cos(t), 8 sin(t)) at t = T.

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Q: 23. Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) =…

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

A: Sol

Q: Find the curvature, torsion and tangent plane for the curve C :1 =1– sint; y = cos t; z = t at point…

A: In this question, we have to find the curvature, torsion and the tangent plane for the given curve…

Q: Use the formula to find the curvature. [i² + ÿ² ]2 where' the dots indicate derivatives with respect…

A: The equation of the given ellipse is x=3cost, y=4sint. Now,…

Q: Consider the following curve 7(1) = (-2sin(e), –V5,2cos() (a) Find the unit tangent vector. (b) Find…

A: The formula to obtain the unit tangent vector for any curve r(t) is given by: The formula to find…

Q: Find the curvature of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the pointt = 0 Give your answer…

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Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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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: 1) T(t) - (cost + 1 sint)i +(int-t cost) J +r'k %3D + rk

A: The arc rate at which the tangent changes direction as the point P moves along the curve is called…

Q: Find the curvature of the curve r(t). r(t) = (3 + 6 cos 9t) i - (8 + 6 sin 9t)j + 6k %3D

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Q: Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) = (4…

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Q: Find the radius of curvature of the curve r=t°i+ 2t´j- - tk at the point where t= 1

A: Since you posted multiple question in this question which are not interlinked so i have solved first…

Q: 1) Calculate the curvature of the position vector r(t) = sintāx + 2costāy + V3 sin t āz is a circle,…

A: Given position vector is  r→t=sintax→+2costay→+3sintaz→ Then unit tangent vector is…

Q: What is the curvature of r(t) (0, 9 sin t, 9 cos t) ?

A: We need to find the curvature of r(t)=0,9sin t, 9 cos t The formula for finding the curvature is…

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

A: The given curve y=e-x4  ,  x=8

Q: Find the curvature of the curver(t) = (4 cos(t), 4 sin(t), 5t) at the point t = 0 %3D Give your…

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Q: Q2/Find the curvature of the curve, r= (4 cos ni+4 sin n j) .n=(In 2t)

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

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

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Q: 1) Calculate the curvature of the position vector F(t) = sin t ax + 2cost ay + V3 sin t āz is a…

A: Formula of Curvature(K) of the position vector r(t):…

Q: Find the curvature of the function y = sin(3x) at x = 0.5. Find the radius of curvature at x = 0.5.…

A: Given function is y=sin3πx and x=0.5   To Find: The radius of curvature at x=0.5 To Find: The center…

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

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Q: Find and completely simplify the formula for the curvature of r(t)=sin(3t)i+cos(3t)j +4tk

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Q: 1) Calculate the curvature of the position vector ŕ(t) = sin t āx+ %3D 2costay + v3 sin t āz is a…

A: To calculate the curvature of the position vector r¯t=sintax¯+2costay¯+3sintaz¯  is a cirlceAlso to…

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

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Q: 6. Find the radius of curvature of the cycloid x= a( t-sin t), y = al 1-cos t).

A: 6. The parametric equation of the given cycloid is x=at-sint, y=a1-cost. First, evaluate the first…

Q: Find the curvature, torsion and tangent plane for the curve C : x = t sin(2t); y = t cos(2t); z = 2t…

A: We have to find the curvature, torsion, and tangent plane for the givne curve.

Q: 5. Find the curvature of the cardioid r= 3( 1+ cos 0 ) at 0= T.

A: Formula: curvature=r2+2r'2-rr''r2+r'232

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: Find the curvature of the curve 7(t) = (t – sin t, 1 – cos t) at the point t 2 |

A: Curvature = k= ||T'(t)|| / ||r'(t)||

Q: 1) Calculate the curvature of the position vector F(t) = sin t ax+ 2cos tay + V3 sin tāz is a…

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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 of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the point t %3D Give your…

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