Let C be the space curve defined by Ř(t) = (2cos t,2 sin t, t). O Find the moving trihedral of C at t = %3D .

Q: Suppose r(t) = ⟨t, 0⟩, for a ≤ t ≤ b, is a parametric description of C; note that C is the interval…

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Q: Find the curvature k for the space curve r(t) = (4 +t)i + tj. %3D Lütfen birini seçin: a. 3/2 b. 2…

A: Given curve is Applying derivative: Applying derivative again:

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A: It is a 3D and we have to draw in a sheet which is 2D. I is a tough task but I will try to draw it…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Let D be the unit disk: x + y² < 1. Evaluate I| 7exp(x² + y²) dx dy by making a change of variables…

A: Given:The integral

Q: Let C be a simple closed smooth curve in the plane 2x + 2y + z = 2, oriented as shown here. Show…

A: Given, The equation of the curve is 2x+2y+z=2. The closed integral is ∮C2y dx+3zdy-x dz Let…

Q: Evaluate the line integral (2 yi + (r- 2)j+ zyzk) · dr where C is the parametric curve r(t) = ti +…

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Q: Given the integral representing the length of the parametric curve x = t,y=t", 0 < t <1 A dt [4¢ + 9…

A: Length of parametric curve , L= ∫abdxdt2+dydt2 dt

Q: Let D ⊂R^2 be a disk containing the origin and assume that g : D → R is a function given by g(x,y) =…

A: This is a problem of multi-variable calculus.

Q: Determine whether the space curve given by r(t) = (t, t 3 , t 2 + 1) intersects the xy-plane, and if…

A: Given the space curve,  r(t)=t,t3,t2+1

Q: Suppose F(x, y) = (3x – 2y)i + 3xj and C is the counter-clockwise oriented sector of a circle…

A: Given, F→(x,y)=(3x-2y)i→+3xj→ Here, M=3x-2y and N=3x radius=3 θ=π3 Limits are 0≤r≤3 , 0≤θ≤π3

Q: Find the curvature of the space curve. r(t) = -10 i + (t + 4) j +(In(cos t) +9) k %3D OK= sect K =…

A: Formula of radius of curvature:      k=r→'(t)×r→''(t)r→'(t)3 First we need to find r→'(t),r→''(t),…

Q: Find the coordinates of the centroid of the curve x = e^t cos t, y = e^t sin t, 0&lt;=t&lt;= pai.

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Q: Find T, N, and x for the space curve r(t) =7i+j,t>0. T(t) = (O i+ (O i

A: Formula for T, N and k are defined as  T=vv, where v=drdt N=dTdtdTdt and k=1vdTdt

Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

A: Length of the curve, rt ,  L=∫abrt˙dt ,    a≤t≤b (a)  Consider the parametrisation of the helix,…

Q: Find the curvature of the space curve. r (1) = -8i + (1 + 4) j + (8 + In(cos t)) k %3D OK = sec t…

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Q: Find T, N, and k for the space curves r(t) = (3sint)i + (3cost)j+ 4tk %3D

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: Sketch the space curve r(t) = i + t2j + t3k and find its length over the given interval [0, 2] .

A: If r=x(t)i+y(t)j+z(t)k then length of r over [a, b] is L=∫ab[x'(t)]2+[y'(t)]2+[z'(t)]2dt

Q: Suppose F(x,y)=4yi +3xyj. Use Green's Theorem to calculate the circulation of F around the perimeter…

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Q: Find the coordinates of the centroid of the curve x = cos t, y = t + sin t, 0&lt;=t &lt;= pai.

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Q: Evaluate ∫c (y+sin x) dx + (z2 + cos y ) dy +x3 dz where C is the curve r(t) = (sin t, cos t, sin…

A: ∫C y+sin x dx + z2 + cos y dy + x3 dz = ∫C y+sin x i + z2 + cos y j + x3 k (dx i + dy j + dz k)…

Q: z+v" = 2 +3: = 2

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Q: Find T, N, and k for the space curve r(t) = i+Tj, t> 0. T(t) = (O i+ (Oi

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Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

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Q: Suppose F(x,y)=(4x−4y)i +3xj  and C is the counter-clockwise oriented sector of a circle centered…

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Q: Evaluate the integral [(3x – 2y + z)ds where C is the curve, C, and C, as shown. 3 y²+ z² 2 G 2* 3…

A: Given that ∫c3x-2y+zds. The objective is to find the integral value. ∫c3x-2y+zds=∫c13x-2y+z…

Q: Suppose F(x, y) 4yi + 7xyj. Use Green's Theorem to calculate the circulation of F around the…

A: Given  F→x,y=4yi→+7xyj→ To calculate the circulation of F→ around the perimeter of a circle C of…

Q: Let C be the positively oriented circle centered at the point zo with radius r>0. Use a…

A: We will first parametize the circle C

Q: Find the Curvature of the space curve r (t) = ti + t? j + t3 k at t = 1. Enter an integer or a fully…

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Q: Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

A: Given function: f(r,θ)=r2*sinθ2Disk description: radius=R0 and center at the origin To find: Average…

Q: Find the curvaturek for the space curve r(t) = (cos(t²))i + (sin(t²))j. %3D Lütfen birini seçin: a.1…

A: we have,r(t)=cost2i+sint2jhere,x=cost2andy=sint2we know…

Q: 7. Given the space curve r(t) = (4 sin t,4 cos t, 10t), Find T, N, B, and T(torsion)

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Q: Let R be the region enclosed by the loop of the t², y = t³ – 3t. parametric curve x =

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Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: To illustrate that the tength of a smooth space curve does not depend on the parameterization used…

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Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: In each of the following cases, define a parametrised curve y : [a, b] → C whose image * is: (a) The…

A: When we deal with contours ,we think about function of two and three variables. Contours in two…

Q: To illustrate that the length of a smooth space curve does not depend on the parameterization used…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: ( 1 ) f α a(s)is a regular differentiable curve, then show that :- (a) kt = -(dT/ds dB/ds), (b)T =…

A: (1. (i. Let  be a differentiable regular curve. Then there exists three orthogonal unit vectors as…

Q: Let C' be the circle of equation a² + (y - 2)2 in counterclockwise direction. a) Find the…

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Q: Find T, N, and k for the space curve r(t) =i+ i, t>0_

A: In this question, we find the unit tangent and unit normal along with the curvature of given r(t)

Q: Find the curvature K for the space curve r(t) = (/3sint)i + (sint)j+ (2cost)k.

A: Let, γ(t) be a space curve. The curvature of the space curve is given by, κ=γ'(t)×γ"(t)γ'(t)3.

Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: Suppose F(x, y) = (4x – 3y)i + 4xj and C is the counter-clockwise oriented sector of a circle…

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Q: Show that the curve r(t) = (ln t)i + (t ln t)j + t k is tangent to the surface xz2 - yz + cos xy = 1…

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Q: Find the coordinates of the centroid of the curvex = cos t, y = t + sin t, 0 ≤ t ≤ p.

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Q: Let C be the curve in space with parametrization r(t) = cos ti + ecoS t j+ sin tk for t € [0, 5].…

A: Given -  To find -

Q: Find the curvature of the space curve. r(t) = (6t sin t+ 6 cos t)i + 6j + (6t cos t-6 sin t)k 1 O A.…

A: Given space curve

Q: Let C be the curve in the plane with parametrization r(t) = cos ti+ sin tj for t e [0, 4T]. Compute…

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