F =< y°,-x² > in the displacement The work done by the force along the path C:y=x from the point (0,0) to (1,1) is

Q: Find the work done by the force F = zi + xj+ yk in moving a particle along the curve x = t y = t²…

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Q: Find the work done by the force F(x,y)=(x - y') i+xy´ j acting on a point while travelling along…

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

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Q: a) Find the tangent plane and normal line of the surface f(x, y, z) = x2 + y?e* + z? = 3 at point P…

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Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

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Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x =…

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Q: a) Find the tangent plane and normal line of the surface f(x, y,z) = x² + y²e* +z² = 3 at point P…

A: Given surface is                                                    f(x, y, z)=x2+y2ex+z2=3 we have…

Q: 9. Find the work done by the force F(x, y, z) = e³i + ln(x)j + 3zk, in moving an object over the…

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Q: Let f : R+ × R → R be the function f(x,y) = 2x + VTy³. (a) Find a tangent vector to the graph of…

A: The given function is: fx,y=2x+xy3 The given point is: 1,1,3

Q: Find the work done by the force F(x, y) = acting on a point along the smooth curve C, where C is the…

A: The given question is from the topic of Advanced Calculus

Q: Find the work that is done by the force F = (x + y)î + xyj – z?k acting on a particle that moves…

A: Convert function into parametric function. Then find work done by doing line integration.

Q: Find the directional derivative of V.U at the point (4, 4, 2) in the direction of the corresponding…

A: We have to find the directional derivative of ∇·U at the point 4,4,2 in the direction of the…

Q: over the curve r(t) = (t, t²,t) for 0<t<1 in 1. Find the work done by the force F(r, y, 2) = (ry, y,…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Determine the work done by the force F"(x,y,z)=(x²y,xy). to move a particle along the line segment…

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Q: The work done by the force F = in the displacement along the path C:y=x² from the point (0,0) to…

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Q: consider the function f(x, y) esin(@) y Find the directional derivative of f at the point (, 1) in…

A: Please refer the attached image for complete solution.

Q: The directional derivative of a function f(x, y, z) = xy² – xz + y² at the point Po (1, –1,0) in the…

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Q: Evaluate fc F • dr, where F = (z, y2, x) and C is parametrized (in the positive direction) by r(t) =…

A: F=z,y2,x and C is the parametrized by r(t)=t+1,et,t2 for 0&lt;t&lt;2. We have to evaluate ∫CF·dr.

Q: The differentiable function f(*, y, z)= 1x² +7y +3z +4xyz tangent vector v, with i = (1,2,3) e R',P…

A: We have to calculate the derivative of f

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

A: Given that: γt=−costi+sintj; t∈0,π F=x2+y2τ, τ is the unit vector tangential to the path. To…

Q: Evaluate work needed to move an object using force F(r, y, z) = 1 i + (2x + 2y) j+ z k along a curve…

A: The force function is given as F (x, y, z) = x i + (2x + 2y) j + z k   Now, the function r (t) is…

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

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Q: Calculate the directional derivatives of functions Inx f (x,y) = x²+ y? in the direction of the…

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Q: Compute the work done by the force along the curve (use defini- tion): 1 F = [3r – y + y] curve is…

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Q: Q5:- a-Solve the initial value problem for r as a vector function of t. d'r (sin t)i- (cost)j + (4…

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Q: f (x, y, z) = arctan(x² + 2y + z) At the point A(0,1,0) along the direction ñ, where n is the…

A: Given that f(x,y,z)=arctan(x2+2y+z)  For a function of three variables f(x,y,z), the directional…

Q: (a) Let f(x,y) = x² – 5xy. (i) Find the directional derivative at (2, 1) in the direction of i = -i…

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Q: Find the work done by the force F = xy i + ( y - x)j over the straight line from (1, 1) to (2, 3).

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Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: Find the work done when a constant force F=16l bs moves a chair from x =2.4 to x =3.1 ft. along the…

A: Solve the following

Q: Use Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R…

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Q: 13. Given the space curve r(t) = (e' cos t , e' sin t , e“), find the tangential and normal…

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Q: A force F acts on a particle that is moving in two dimensions along the semicircle x = 1 – cos 0, y…

A: Given the forces on a particle that is moving in 2D along the semicircle x=1-cosθ, y=sinθ, 0≤θ≤π.

Q: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…

Q: Evaluate the line integral r(t) = (sin t, cos t, t), F · dr, where F(x, y, z) = −3xi + 2yj + 4zk and…

A: Given:- Fx,y,z=-3xi+2yj+4zk rt=sint,cost,t To find:- ∫cF.dr , where c is given vector rt ,0≤t≤3π2

Q: Evaluate the line integral fe F - dr, where F(z, y, z) = -ri + 4yj + 5zk and C is given by the…

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Q: Find the work done by force F(x, y) = 2yi + 3xj + (x + y)k in moving an object along curve r(t) =…

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Q: e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward…

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Q: a) Find the directional derivative f (x, y, z) = x In(y+z) at point P (2, e, e) in the direction of…

A: We have to find directional derivative of vector f in the direction of vector v:

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

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Q: Find the work done by the force, F(x,y) = 2xyi+ 4x*y, along the curve C given below in the counter…

A: We have to find the work done by the force Fx,y=2xy3i+4x2y2j, along curve C in the counterclockwise…

Q: (b) Find the tangent plane and normal line to f(x, y, z) = x²y+y?z+ z2x at the point (1, – 1, 1).

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Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: %3D the tangent plane at the point with ry coordinates (x, Y) = (0, 1).

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: E For the surface f(x,y, z) = tan(xy + %3D at (0,1,0) in the direction of ü = i- 2j +2k; (3) the…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Verify Stokes' theorem for F = z²i – y²j and the curve C is the square in the xz-plane from (0,0, 0)…

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Q: Find the work done by the force F(r) = x2 +1 in moving a particle along the T-axis from r = 0 to r…

A: The work done by a variable force F(x) in moving a particle along the x-axis is given by the…

Q: nd a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

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