$2 5. Find the unit tangent and the principal unit normal vectors for the helix given by r(t) = (2 cos t) i + (2 sin t) j+ tk. 6. Find the curvature of r(t)= ti+t2j + t k. 7. Find the curvature of the plane y = cos() +e 2x at r 0. 8. Find the maximum curvature of y In . ck aveerune, chece cleiractie eluvahe +ozors 9. Find the tangential component ar and normal component an for the curve given by r(t) 3ti tj+ tk. 10. Let a(t) = 2t i + e' j + cos(t) k denote the acceleration of a moving particle. If the initia v(0) = i+ 2j-k, find the particle's velocity v(t) at any time t. V2 x (a) Find the domain of f(x, y)=In(-1) (b) Sketch the graph of f(x, y) = 6 -2y 12. Find the limit of show it does not exists.

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A: The given curve is: r(t)=sin 2t,cos 2t, cos22t

Q: Find the curvature of r(t) = at the point (9, 1, 1).

A: Given: r(t) = <9t, t2, t3 >at the point (9, 1, 1).

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A: Given: r→(t) = ln t, ecos t, t2

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Q: 2. Let a(t) = (3t – t³, 3t², 3t + t³), for t e R. (i) Calculate the equation of the osculating plane…

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A: Given function is rt=3cost ax+4sint ay+ t az To find curvature and radius of curvature

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A:

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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 +…

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

A:

Q: Find the curvature K of the curve at the point P. r(t) = 1/2t2i + tj + 1/3t3k,    P (1/2, 1, 1/3)

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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 + t…

A: r(t)=3cost, 4sin t,t, t=π2 find r'(t) and r''(t) r'(t)=-3sin t,4cos t,1r''(t)=-3cos t,-4sin t,0 To…

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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…

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Q: Q11

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Q: Find the unit tangent vector T(t) and the unit normal vector N(t) and the curvature K for r(t) = (t,…

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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…

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Q: Find the curvature K of the curve at the point P. r(t) = t2i + tj + t3k,    P (1/2, 1, 1/3)

A: we have been given r(t)=t2i+tj+t3k

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