Given the curve r (t) = (2 sin t, 2 cos t, t) where 0

Q: Find the point on the curve r(t) (12 sin t)i – (12 cos t)j + 9tk at a distance a) 5n units and b)…

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Q: Find the arc length (s) of the curve r(t) = (- e*, 2e, – 4e*) for 0 <t < In(3) S =

A: To find the arc length of the curve

Q: The arc length of the curve r= cos 30 with 0<0<n is

A:

Q: ) Find the arc length of the curve x = cost + tsint, y = sint – tcost on the given interval 0 < t <…

A: Here we have to find the arc length of the curve x=cost+tsint, y=sint-tcost, on the given interval…

Q: If the arc length s of the curve C : r (t) = cos(t)i + sin(t)j + from t = 0 to t = b is 20 units,…

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Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: Find the arc length of the curve r(t) = (4t^2, 2(sqrt4)t, ln t), for the domain of t between 1 and…

A: We have to find Arc length.

Q: Given R(t) = (1 – 4 cos t) î + 3 cos ĵ + 5 sin t k̂, find the arc length of the portion of R(t)…

A:

Q: Given r(t) = et sin t i + et cos t j + v2etk, a) find the arc length function for the curve measured…

A: (a) Given a curve rt=etsinti^+etcostj^+2et k^, to find the arc length of the curve measured from the…

Q: = cos' t, y= sin’ t, z=2, where 0Sts“ 2 Find the arc length of the curve x

A: Given curves are, x=cos3t , y=sin3t, z=2.

Q: Find an arc length parametrization of r(t) = (e' sin(t), e cos(t), 2e*). r:(s) =

A: Calculate the derivative for r(t).

Q: Find the arc length L of the graph of r(t). r(t) = 5 cos(t)i + 5 sin(t)j + tk, 0 <t < 2n L

A:

Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+2tk from t = 0 to t = b is 20 units,…

A: The arc length of a parametric curve defined by the vector r→=f(t), g(t), h(t) defined over the…

Q: Find the arclength of the curve in the given interval. x = 3 cos? t , y= 3 cost sin t , 0 s<t <t

A: solution is written in below steps.

Q: Find arc-length of the following curve 0 <t < 2 x = sin (t) Y = cos'(t)

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Q: Given that v1+ tan x dx represents the arc length of some curve defined by y= f(x) on 0, A,…

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Q: Use the arc length formula 2 dx 2 L = dy dt dt dt to find the arc length of the curve. x = cos 12t,…

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Q: For the curve x = sin(t) - tcos(t), y = cos(t) + tsin(t), z = t2, find the arc length between (0, 1,…

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Q: Calculate the arc length of the indicated portion of the curve r(0) r(e) = 2 (1 + cos e )

A: The given curve is Consider the curve is taking a complete revolution i.e. from 0 to 2π So,…

Q: Find the arc length over the given interval. 8. r(t) = (cos(3t), sin(3t)) [0, z] over 9. r(t) =(-t,…

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i +2 sin(t)j+tk, 0<t< 2m L =

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j + 12t k at a distance 26paiunits along…

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Q: Find the arc length of the indicated portion of the curve: r(t)=(e' cost)i +(e' sint)j+e'k, In 4…

A: Given:rt=etcosti+et sintj+etkInterval 4≤t≤0Arc length:L=∫abdxdt2+dydt2+dzdt2 dt

Q: Find the arc length of the curve y = e*te, o<x < 2.

A: Given equation - y = ex+e-x2               ..............(1)Formula for finding the arc length of a…

Q: Find the arc length for the curve r(t)= cos(t)i+sin (t) j + tk , 0<t<2n .

A:

Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0≤ t ≤ 2π

A: Given :

Q: Given R(t) = (1 – 4 cos t)î + 3 cosĵ + 5 sin tk, find the a. arc length of the portion of R(t) from…

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Q: Find the arc length of the curve F(t) = (cos" (t),0, sin (t)) from t 0 to t

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Q: cos(7t), 3t >. Find the arc length parameter s(t) with base point at P(t0) where t0 = 4.

A: Here is solution

Q: Find the length of the curve 7 (t) = (ei cos(;),ei sin(;),ei) for 0 <t<4. Arc length =

A:

Q: Find the arc length of the curve r(t)= for 0 ≤ t ≤ 3.

A: Apply arc length formula

Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+ 3tk from t 0 to t = bis 20 units, then…

A:

Q: Find the arc length L of the graph of r(t). r(t) = 9 cos(t)i +9 sin(t)j + tk, 0≤t≤ 2π

A: This is a problem of vectors and integration. Based on concepts and formula of arc length we will…

Q: Find the arc length L of the graph of r(t). r(t) = 6 cos(t)i + 6 sin(t)j + tk, 0<t< 2n 0 <t< 2n L =

A:

Q: Find the arc length (s) of the curve 7(t) = (e*, 4e", - 2et) for 0 <t < In(5) |

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

Q: Find arc length function for the given curve. 11. r(t)= (sinr', cos ?) 12. r(1) = (e", 2e' , t)

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Q: 21. Find the arc length of the curve x = cos' t, y= sin' t, z=2, where 0<t<. 2

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Q: Find the arc length L of the graph of r(t). r(t) = 4 cos(t)i + 4 sin(t)j+ tk, 0<t< 27 L

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Q: Find the arc length function for the curve ř(t)= (cosht,sinht,t) taking a=0.

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Q: The arc length of the curve r = cos 30 with 0<0<n is

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Q: Find the arc length L of the graph of r(t). L r(t) = 12 cos(t)i + 12 sin(t)j + tk, 0≤t≤ 2m

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Q: Find the point on the curve r(t) = (5 sin t)i + (5 cos t)j+ 12tk at a distance 26™ units along the…

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Q: Find the arc length L of the graph of r(t). r(t) = 10 cos(t)i+ 10 sin(t)j+ tk, 0<t< 2n

A: To find the arc length of the given graph.

Q: Given R(t) = (1– 4 cos t)î + 3 cosĵ + 5 sin t k, find the a. arc length of the portion of R(t) from…

A: Given the vector :

Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0<t< 2n L =

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Q: Find the arc length (s) of the curve r(t) = (5e“, – 2e“, – 3e“) for 0 <t < In(2) S =

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Q: Use the arc length formula 2 dy dt dx L = dt + dt to find the arc length of the curve. x = cos 61, y…

A: Arc length is the line integral of the curve along the given range. It is basically the length of…

Q: Consider the curve r(t) = (e' cos(at), e' sin(nt), e'). (a) Compute r'(t) and r'(T). (b) Compute…

A: Consider the curve r(t):