( 1 ) f α a(s)is a regular differentiable curve, then show that :- (a) kt = -(dT/ds dB/ds), (b)T = (B.dN/ds) (c) k = -(T- dNd) where k , T considered curve respectively. %3D and are the curvature and the torsion of the

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: 2:(b) Find the exact arc length of the curve x=e"(sint+ cost), y=e" (sint – cost) over the interval…

A: Given

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A:

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A: Basic identities of differentiation and vector calculation are used

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A:

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A:

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

A:

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Q: (a) Given that the transition curve of the highway is modelled after the curve y=4sin x-sin 2 x.…

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A: Sol

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A: Use formula of radius of curvature

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Q: For KEIRT and TEIR construct Co-Curve Y: IR→IR³ with constant Curvature K and constant torsion T

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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.

A:

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Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

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A:

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

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

A:

Q: Q2. A particle moving along the curve R(t)=(cost +1 sint)i + (sint -t cost)j,find acceleration…

A: Solution:

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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: At what point does the curve have maximum curvature? y = 9 ln(x) (x,y) =? what happens to the…

A: we are given we can use formula now, we can plug it and we get

Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…

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Q: Find the curvature of he curve :  at x^2/3 at x=1

A: GivenLet f(x)=x23To find the curvature of the given curveFormula:ρ=1+f'(x)232f''(x)

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A: Given:

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Q: Find the arc length of the parametric curve: x = e'(sint + cos t), y = e'(cost - sint) OstsIn3

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