Find the length of the following three-dimensional curve. r(t) = (sin t, cos t, 4t), for 0sts5 L = (Type an exact answer, using radicals as needed.)

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Q: 3) Find the length of the curve r= cos (0/3), 0< 0 <"/4:

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Q: Find the length of the following three-dimensional curve. r(t) = (cos t, t, sin t), for 0sts8 L3D…

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Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3 %3D

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Q: Find the length of the following three-dimensional curve. r(t) = (sin t, t, cos t) , for 0 st<5 L=…

A: Directly use the formula for the length of a curve in three dimensions.

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A: The formula for finding the length of the curve is explained in step 2 with a general observation…

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A: Use the formula for the length of curve in parametric form.

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A: Given,

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A: we are given the curve  r→(t)=e5t,-4e5t,-2e5t =e5ti-4e5tj-2e5tkwhere 0≤t≤ln5

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Q: Consider C(t) = -2i + 2eit, 0 ≤ t ≤ 2π. Is C an arc? Is C a simple arc? Is C a simple closed curve?

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Q: Find the length of the following curve using methods for parametric curves. x = 4 sin t y = 4 cos t…

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Q: Find the length of the following two-dimensional curve. r(t) (2 cos t+2t sin t,2 sin t- 2t cos t),…

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Q: Find the length of the following three-dimensional curve. r(t)= (sin t, cos t, 2t), for 0sts4

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Q: Find the length of the following two-dimensional curve. r(t) = (5 cos t, 5 sin ), for 0sts

A: Recall: Length of the Parametric form :L=∫t=at=bx'(t)2+y'(t)2 dt

Q: Find the length of the following two-dimensional curve. r(t) = (12t – 2,16t +2), for 0sts1 The arc…

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Q: Find the length of the following​ three-dimensional curve. r(t)=cos t, sin t, 3t​, for 0≤t≤2

A: Given that rt =cost,sint,3t  for 0≤t≤2 find the length

Q: Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos…

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Q: Find the length of the curve: r = /1+ cos(20),0ses 2n

A: The length of the curve is given by the formula ∫abr2+drdθ2dθ  ,       where a≤θ≤b

Q: Find the length of the curve #(t) = et cos(t), y = e* sin(t) for 0 <t < 5. %3D %3D Give an exact…

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