Evaluate fe kz ds where k is a constant and is the circular helix with parametric equations T = Cos t. u = sin t and z = t where 0 < t < 27

Q: Find the surface area of the solid generated the parametric curve: x = cos?t, y = sin²t, 0 <t s, is…

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Q: dy dy and for the parametric equations: x = 2t2 +1 y = t at t = 1 Find dx dx? dy dy dx? %3D

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Q: Find the arc length of the parametric curve. x = 8 cos(t), y = 8 sin(t), z = 6t; 0 <t< T L = %3D

A: To find the arc length of the parametric curve.x=8 cost, y=8 sint, z=6t; 0≤t≤π

Q: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), z = 24t; 0<t< T L =

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Q: I. Let C be the parametric curve with parametric equations x=t(t² + 1)-¹/2 te [-3,3] ly: = 2t - 2…

A: There are two points at where the tangent line is horizontal

Q: 6. Evaluate y sin(z) ds, where C is the circular helix given by the parametric equations x = cos…

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), % = 3t; 0 < t < T L =

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Q: Find the arc length of the curve on the given interval. Parametric Equations      x = e−t cos t, y =…

A: We have given;

Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

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Q: I. Let C be the parametric curve with parametric equations [x = t(t² + 1)-¹/2 te [-3,3] y = 2t - 2…

A: We have to set up the integral that gives the arc length of C.

Q: Find the arc length of the parametric curve. = 14 cos(t), y = 14 sin(t), z = 48t; 0<t <T

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Q: Find the area under the curve for the parametric function defined by the equations x(t) = -2 cos t,…

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Q: Find the length of the curve with parametric equations x = e' · cos t, y = e' sin t, with 0 <t <…

A: Given x = et.cos(t) y = et.sin(t)

Q: Set up but DO NOT EVALUATE the integral to find the length of the curve described by the parametric…

A: We have given parametric equations  xt=cos2t,yt=sin5t  for   0≤t≤π.

Q: What is the arc length of the given parametric curve x = cos3t; y = sin3t;0 <t< 2n. O 37 None of…

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Q: Evaluate the cylindrical coordinate integral. 1/2 18 1/r cos 0 dz r dr d0 0 9 1/?

A: Given that triple integration problem or cylendrical coordinate problem .we use simple integration…

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Q: Find the arc length of the parametric curve. 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T L=

A: Here we have to find the arc length of the parametric curve.

Q: 10. Find the arclength of the curve given by parametric equations x = r?, y = 2/2r, z = In(x²), 1<t<…

A: Given is x=t2, y=22t, z=ln (t2), i.e.z= 2 ln t,    1&lt;t&lt;2 The main objective is to compute the…

Q: Consider the parametric equations below. x = t sin(t), y = t cos(t), 0 st s 1/2 Set up an integral…

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Q: Q1 Consider the plane curve defined by the parametric equations x = p + t sin(t),y= p² + t cos(t).…

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Q: 5. For the Parametric curve x = a(t – sint), y = a(1 – cost) where 'a' is a constant. Find y d?y at…

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Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Consider the parametric equations t3 + 2t, y = e' +t te [1, 10] Find an integral expression for the…

A: We know that area enclosed by x-axis and portion of curve y=f(x) in [a,b] is

Q: Consider the following parametric curve: S æ(t) = sin(t) y(t) = 1+ cos(4t) for Sts -- %3D whose…

A: Answer

Q: Find the arc length of the parametric curve. x = e', y = e, z = v2t; 0<t < 8

A: Here, the given parametric equation is: x=et, y=e-t,z=2t, 0≤t≤8 The formula for the arc-length is…

Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

Q: 20. Evaluate Vx2 + y? ds where C is the curve with parametric equations x = 4 cos(2), y = 4 sin(t),…

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Q: Find the arc length of the parametric curve. x = 14 cos(t), y= 14 sin(t), z = 48t; 0<t<T L

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Q: Find the arc length of the parametric curve. 8 cos(t), y = 8 sin(t), z = 6t; 0<t<T x = L =

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Q: Find the arc length of the parametric curve. x = 7 cos(t), y = 7 sin(t), 24t; 0<t< T Z = L =

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Q: Given: R(t) = (cos t + t sin t) î + (sin t – t cos t) ĵ + t?k ,t>0 Find parametric equations for the…

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Q: Find the arc length of the parametric curve. x = 8 cos(t), y = 8 sin(t), z = 6t; 0 <t < T L = ||

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Q: Find dy/dx at t=1 by the given parametric equations, x=r and y=t, dy/dx is Blank 1. The answer must…

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Q: Find the arc length of the parametric curve. x = 24 cos(t), y = 24 sin(t), z = 7t; 0<t< T L =|25

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Q: Find the arc length of the parametric curve. x = cos' t, y = sin° t, z = 2; 0 < t < T/2

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Q: Consider the parametric equations below. x = t sin(t), y = t cos(t), 0 ≤ t ≤ ?/3 Set up an integral…

A: To set the integral

Q: At what points does the helix  r(t) = sin(t), cos(t), t  intersect the sphere  x2 + y2 + z2 = 82?…

A: Answer is mentioned below

Q: Consider the curve given by the parametric equations x (t) = sin t – t cos t and п dy 3 dx y (t) cos…

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Q: Find dy/dx at t=1 by the given parametric equations. *=t² and y=t°. dy/dx is Blank 1. The answer…

A: Given,           The parametric equations are x=t2 and y=t3.To find : dydx at t=1

Q: Find the arc length of the parametric curve. x = 4 cos(t), y = 4 sin(t), z = 3t; 0<t< T L =

A: Given parametric curvex=4 cost , y= 4 sint  , z=3t ;  0≤t≤π

Q: A thin wire has the shape of the curve C traced by r(t) = cos(nt)i + tj+ (sin(nt) + 5)k. 0 st<1 (a)…

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Q: Consider the parametric equations t3 + 2t, y = e' +t te [1, 10] Find an integral expression for the…

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Q: Consider the curve Cwith parametric equations Sa(t) = t3 – 3t +1 lu(t) = t(t + 1) | lefined for t…

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Q: cos(u) dx. int_ccC [2x*cos(y) \ dx \ - | x^2 sin(y) \ dy] x? sin(u) dul if C is the curve x^4+y^4=1,…

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Q: dr 2 +r² dt, 2 L = dz' (dt. dt, x = rcos(0) y = rsen(0).

A: Given a parametric curve x=rcosθ, y=rsinθ, z=z(t)  for a&lt;t&lt;b To show…

Q: Find the arc length of the parametric curve. x = 24 cos(t), y = 24 sin(t), z = 7t; 0<t< T L

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Q: Find the arc length of the parametric curve. x = 3 cos(t), y = 3 sin(t), z = 4t; 0<t<+ L =

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Q: 26 Given the parametric equations x=4cos? r and y = 5sint. Find dy when t= dx

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