The curvature of a(t) = 3t e₁ + 4sin t e₂ + 4cos t ez is

Q: Consider the given plane curve. Find the point on the curve where the curvature is maximised. What…

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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: 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: 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: Let C(t)=((1/2)cos(t),(1/2)sin(t)) be the circle of radius 1/2 when t is from 0 to 2pi What is the…

A: Given that C(t)=12cost,12sint be the circle of radius 1/2 where t is from 0 to 2π. Here C(t) is a…

Q: Consider the helix r(t) = (cos(-2t), sin(-2t), -4t). Compute, at t = 7: A. The unit tangent vector T…

A: We can find unit tangent , normal , binormal vector and Curvature .

Q: Write a formula for curvature in terms r1(t) and t1(t)

A: The rate of change of direction of the curve with respect to the distance along the curve is defined…

Q: Find the curvature of the vector function r(t) = (4 cost, 4 sint, t) for t = RIN 2

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Q: Find the curvature of the curve given by r(t) = (4sin t, t, 4 cos t).

A: To find - Find the curvature of the curve given by rt = 4sint, t, 4cost     Formula used -…

Q: Calculate the mean curvature of the catenoid 2²+ y? 2= a1 a

A: The complete solutions are given below

Q: Calculate the mean curvature of the catenoid

A: Given; z=ax2+y2a

Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

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

Q: The curvature of r = 1+ cos 0, 0: 2 2/2 5 2/2 3/3 2 3/3 3.

A: Given: r=1+cosθ,θ=π2 κθ=2f'θ2+fθ2-fθf"θf'θ2+fθ232   r=f(θ)r=1+cosθ f'θ=-sinθf"θ=-cosθ

Q: The curvature of the curve (t) = 6t, 6t+1, sin2t at t= TT 0 1 8. 01 01 18 O 2 1/2

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Q: (b) Find principle curvature of X(u, v) = (u cos v, u sin v, bv).

A: Given that X(u,v)=(ucosv,usinv,bv) Take the derivative with respect to u, dXdu=(cosv,sinv,0) Take…

Q: 5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1);…

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Q: A particle moving in the x-y plane has a position vector given by r = 3/2t²i + 2/3t³j, where r is in…

A: A particle is moving in the x-y plane has a position vector given by r=32t2i+23t3j, where r is in…

Q: Consider the helix r(t) = (cos(-4t), sin(-4t), 3t). Compute, at t = :

A: The parametrization of the curve is given asTo find the unit tangent, unit normal, binormal and the…

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 k(t) of the curve r(t) = (-1sint) i+(-1sint)j+(-4 cos t) k %3D

A: Given : rt=-sinti+-sintj+-4costk To find : curvature κt Curvature is given by  κt=r't×r"tr't3…

Q: The curvature of the curve 7 (t)= (2t, 2t+ 1, sin2t) at t= TT is 4. 1 18 O 1 1/8 1/2 O O O O

A: The given curve is r(t)→=2t,2t+1,sin(2t) We know that the curvature κ(t) for r(t)→ is given by the…

Q: Let r(t) = (sin t-t cos t)i + 7j+ (cos t+t sin t) k . Find the following: (a) Unit tangent vector T…

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