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Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…
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Q: Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the…
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Q: What are the critical points for the plane curve defined by the equations æ(t) = sint + cos(t), y(t)…
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Q: find y'' for the curve cosx-siny=4
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Q: Let C be the curve defined by r(t) [6 cos(t) – 5 cos (t), 6 sin(t) – 5 cos(t) sin(t), cos(t)] for 0…
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Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…
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Q: Consider the curve x = et-5 cos t, y = et-5 sin t, 0 <t < 2n. a) Find the values of t where the line…
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Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…
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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =
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Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…
A: Given: y=18x2−lnx if 18≤y≤e28−1 ⇒f(x)=18x2−lnx if 1≤x≤e The arc length of the portion of the graph…
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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l
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Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…
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Q: 3. Find the length of the curve y = In (cos x), 0 <x <
A: we have to find length of the curve
Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…
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Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…
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Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=
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Q: Let C be the curve parameterized by r(t) = (cos(t), sin(t), /3t), 0 <t < 1/2. Calculate 1. |r'(t)| =…
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Q: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)
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Q: A particle moves in the xy-plane in such a way that its path is defined by x = et cos t and y = et…
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Q: Find the lengthof the curve r = a sin² (0/2), 0 0
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Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for π/2≤ t ≤π/2 Find out dy/dx…
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Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…
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Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.
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Q: Find the arclength of the curve y = * - In x if < y s-1. Do not simplify your answer for this…
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Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 In(cos(t)) k, osts n/4
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Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…
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Q: Find the arclength of the curve x = 3 cos(5t), y = 3 sin(5t) with 0 <t< 20 %3D
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Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.
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Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6
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Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.
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Q: Show that 22 dz = 0 1 – cos(2) whenever y is a closed simple smooth curve contained in a very small…
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Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…
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Q: Find the arclength of the curve: y = 5(x +2)3/2, 2<x<7
A: Given: Find the arclength of the curve : y=5(x+2)^3/2 ,2<=x<=7
Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7
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Q: Find the derivative dydx of the hyperbolic spiral r=aθ.
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Q: Suppose a curve is defined by: x/x-y=y2-1 FIND dy/dx
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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4
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Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.
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Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =
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Q: 7- Find the leng thof the Curve arce 34 from to y=4
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