Calculate the circulation of the field F around the closed curve C. Circulation means line integral F = - 6/7 x 2y i -6/7  xy 2 j; curve C is  r(t) = 7 cos t i + 7 sin t j, 0 ≤ t ≤ 2π     - 12     - 12/7     - 6     0

Q: Let 7 (t) = (t + 5, 5e“, 3 sin(5t)) Find the unit tangent vector T (t) at the point t = 0 T(0) = <

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: A vector field F = x(x² – y²) + ŷ(2xy + y?) a) f d.č =? c on the closed curve in the figure b)…

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Q: y² cos(xy?) – ay sin(æ²y) Let it be 7 : R² → R², (2ary cos (ay?) – ža² sin(a²y)/ a vector field.…

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Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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Q: Let r(t) = (-3t³-4, -3e¹, 5 sin( - 3t)) Find the unit tangent vector T' (t) at the point t = 0 T(0)…

A: r(t)=&lt;-3t3-4, -3e4t, -5Sin(-3t) &gt;

Q: Verify if the vector field F = (x° cos(4y), -x sin(4y)) is conservative and evaluate the line…

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Q: late the F= (x - y) i - (x 2 + y 2) j; C is curve from (4, 0) to (-4, 0) on the upper half of the…

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A: The given scalar function is, f(x,y)=xsiny2. Gradient of this function is F=siny22xycosy2. The…

Q: Let 7(t) = (– 5t4 – 4, – 2e“, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0 T (0)…

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Q: Given a velocity field: V = 1.8 ( rz (1-sin²(0))) er + 2.8 (1-cos2(0)+ rz) eg +1.8 ( rz tan(0)…

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Q: Calculate the flow in the field F along the path C. F = (x - y) i - (x 2 + y 2) j; C is curve from…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: In(t + 4) sin2t Given the vector valued function 7(t) = (e-3t, t a) Find the domain of 7(t). b) Find…

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Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

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Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

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Q: 3. (a) Given the vector valued function r(t) = 4 cos zti + 4 sin atj + tk. Find the position vector,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Consider the vector field F(x, y) = (3y²+ 4x, 5y sin(x)). (a) Calculate curl F at the point (0,…

A: The curl of a vector field F = (P, Q) in two dimensions is given by the formula:∇×F=∂Q/∂x-∂P/∂yHere,…

Q: a) Calculate a) b) Calculate the lineintegral F dr.

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Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of x+1 y…

A: Consider the given function F(x,y).