Find the curvature and the radius of curvature at the point t = 0. I = e' cos(t), y = e' sin(t), z = 9e* K. || ||

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: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

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: Pind the curvature x of the curve given by 7(()- (V2)i+ (e)j+(e)k, at the point P(0, 1, 1),

A: Curvature K = |r' x r"|/|r'|^3

Q: Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).

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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.

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: (1 point) Find the curvature (t) of the curve r(t) = (4 sin t)i + (4 sin t)j + (5 cost) k

A: we will find the required solution.

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: 8. [*] for position vector (t-1, 3-2t, 4t-t') find [*] the unit tangent [**] the unit normal, the…

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Q: Consider the curve r(t) = (e' sin(2t), e' cos(2t), 2e*). (a) (b) (c) Find the osculating plane of…

A: Solution: The curve is r→t=etsin2t,etcos2t,2et

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 the radius of curvature at any point x = - of the curve

A: Given,             y=4sin2x-sin4x at  x=π4