Using spherical coordinates, calculate the divergence of the following radial vector functions (a) F = rî. (b) F = r"f. (c) F = e¯ar² î, where a is a constant.

Q: Example Determine the unit tangent vector for r(t) = (t,t³,t5) at the point P = (1,2,3).

A: The vector is: .To Do:We have to determine the unit tangent vector at the point P=(1, 2, 3).

Q: Determine the domain of the vector function r() = cos(4t) i + 7in(t - 5) J - 10 Evaluate if the…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: #6 Suppose the position of a projectile is expressed by the vector-valued function Describe how you…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: For the curve R (t) = (Sin2t, t, cosat) Find the unit tangent vector.

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Q: Let the velocity vector be v(t) = (4t°, –6 sin(3t) , 9 exp(3t)) and the initial position vector be…

A: The position vector can be computed by taking the summation of velocity vector and initial position…

Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

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Q: Ifr(t) = (sin t , cos t, 29- t), then determine a vector that is perpendicular to both unit tangent…

A: Given: r(t) = sin t, cos t, 29-t To determine: A vector that is perpendicular to both unit tangent…

Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: Derivatives of vector-valued functions Differentiate the following function.

A: We have given the function;

Q: let angle thetha be measured from x1 axis counterclockwise to a line drawn normal to the boundary…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t) , sin(3t) , sin( when…

A: Given r(t)=cos(t) , sin(3t) , sin(t) Compare it with r(t)=x(t) , y(t) , z(t) to obtain…

Q: Let r(t) = (-4t¹ - 4, 4e-2t, sin(-3t)) = Find the unit tangent vector T(t) at the point t T (0) = 0.…

A: Given; r(t)=<-4t4-4, 4e-2t, sin(-3t)>.

Q: Sketch the curve which has the vector equation r(t) = cos ti + tj.

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Q: Find the tangential and normal components

A: Given,

Q: 4. Find the unit tangent vector T(t) for the vector function: r(t) = .

A: To find the unit tangent vector.

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

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Q: 2) Consider the vector function r(t) = (sin (t), −3t, cos (t)). Analyze the function, then sketch a…

A: The given function is r(t)=sinπ2t,-3t,cosπ2t Find the value of r(t) for different values of t. t…

Q: Consider the following equation. (y - x)² + 2 = xy - 3 Check that the point (2, 3) lies on the…

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Q: Given u(t) = (e',e-t). a) Find: (i) u'(t) (ii) u"(t) b) Find the unit tangent

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Q: A point moving a long a curve whose position vector is R(t)=(t sin t +cost)i+(sin t-t cost)j+4 k;…

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Q: Find an equation of the plane tangent to the Bohemian dome S described by the vector function R(u,…

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Q: Calculate the velocity and acceleration vectors, and speed for when t = Speed: 11. Velocity:…

A: To calculate the velocity and acceleration vectors, and speed for .

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Given that, gu,v=u2e-v,8,0 and v=3i+4j. Find the value of ∂g∂u and ∂g∂v at the point (8,0).…