z?i + x²j + y²k, find the curl of F and the component of curlF along the tangent vector to the curve x = cos t, y = sint, z = t at the point (1,0, 0). 3. Given F = %3D

Q: Verify Stokes's theorem for F =, where C is the curve C: x² + y² = 4, z = 2

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Q: At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t): = 7 cos(t)i…

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Q: The integral that represents the length of the curve 7(t) = (t, cos (2t3/2), sin (2t3/2)), where 0st…

A: To represent the integral for the arc length of the curve given by r→(t)=t,cos(2t32),sin(2t32)where…

Q: 6. Determine the values oft between 0 and 27 such that the tangent vector to the cycloid r(t) = (t –…

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

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Q: Find the equation of the plane tangent to the surface f(x,y) = x In(x y) at the point (1, e).

A: We will find the equation of tangent plane to the given surface.

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Reparametrize the curve with respect to arc length measured from the point where t = 0 in the…

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Q: Find the derivative of ƒ(x, y, z) = xyz in the direction of the velocity vector of the helix r(t) =…

A: Concept: A vector is a directed line segment whose length is the magnitude of the vector and with an…

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Q: For the curve x = cos t , y = sin t , z = t, find a. an equation of the tangent line at the point…

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Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4…

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Q: Find the work done under the influence of the force E = 3xyi – 5zj + 10xk along the curve x= t² + 1,…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

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Q: Find the directional derivative of the function if f (x, y, z) = 3e* cos(yz) at point %3D (0, 0, 0)…

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Q: Find the unit tangent vector to the curve defined by 7(t) = (5 cos(t), 5 sin(t), 4 sin (t)) at t = 3…

A: We find unit tangent vector of given curve at t=π/3

Q: Find the tungent Irne of where C: F) = is parallel to xy- plane

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Q: Let f(x, y, z) = 3ex cos(yz). a) Find the directional derivative of f at P(0, 0, 0) in the…

A: Given , fx,y,z=3ex cos4zwe have to find directional derivative of f at p 0,0,0 in the directionof…

Q: Find the vector equation of the tangent line to the curve given by 7(t) = sin ti + cos (2t)j + tan…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: (5) Find the equation of the tangent plane to z = 1² + xy +3y* at r = 1, y = 1.

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

Q: Find a parametrization of the tangent line at the point indicated. r(t) = (1 - t4, 4t, 5t), t = 2…

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Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: Find the derivative of f (x, y,z) = xyz in the direction of the velocity vector of the helix…

A: Answer and explanation is given below...

Q: Find an equation for the tangent plane of z 3.xy? + y + 2 at the point (-1, 1, 0).

A:

Q: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

Q: Find a unit tangent vector to any point on the curve x = a cos wi, y = a sin wt, z = bt where a,b,w…

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Q: For the function f(x,y)=4e^(4x)sin(y), find a unit tangent vector to the level curve at the point…

A: Consider the given function, fx,y=4e4xsiny now, find the partial derivatives,…

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Q: Consider the curve C in R3 given by: F(0) = (sin 0 + 0) î+ (sin 0 – 0) ĵ+(-V2 cos 0) k, para 0<osa…

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Q: Find the directional derivative Du f(-3/8,1) for the function f(x, y) = cos(T(4x + 2y)) in the…

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Q: The directional derivative of xy f(x, y) = x + y) at (1, 1) in the direction of the unit vector at…

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Q: Find an equation of the tangent plane to the paramelric curve given by R(u, v) = ((3 + sin v)sin u,…

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Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , e" cos u , e¯º ) at the point where u…

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Q: Find the tangent plane to the function f(x, y) = sin(xy?) at (a,. Is it parallel to the plane 2x- 3y…

A: fx, y=sinxy2 Partially differentiating with respect to x, we get fxx,…

Q: A force F acts on a particle that is moving in the plane along the semi-circle parameterized by 7(t)…

A: Work done W=∫CF.ds=∫abF(r(t)) . r'(t)dt   Where curve C is given by parametric equation r(t)

Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the equation of the plane tangent to the surface f(x, y) = x In(x y) at the point (1, e).

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Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

A:

Q: 3. Find the directional derivative of the function f (x, y)= sin (xy) at a point -2i +j in the…

A: The given function: f(x, y)=sin2(xy)P=34, πu→=-2i^+j^5

Q: Find the directional derivative of the function f(x, y) = tan-(/xy) + li + 2j. Note that In(1 + xy)…

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