The gradient vector field of f(x,y)=cos(x) - 2sin(y) is: O1. f(x,y)= cos(x) i - 2sin(y) j II. f(x,y)=-sin(x) i - 2cos(y) j III. f(x,y)= sin(x)i - 2cos(y) j ON.f(x.y)=-sin(x) i + 2cos(y) j

Q: Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.

A: Use the Gauss’ Divergence theorem,: Use the Gauss’ Divergence theorem,

Q: Calculate the gradient ∇f, where f(x, y) = ln(x2 + y2) (here (x, y) ̸= (0, 0)).

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Q: 3. Find the directional derivative of the given function f at the given point P in the direction of…

A: 3. From the given problem:   fx,y,z=x2+y2+z2 ; p1,2,2 ; a=3,2,1   As we know that the expression for…

Q: Find the f(z) = u(x, y) + j v(x, y) for which X b) u = e cosy most general analytic function

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Q: e R?, whe W -) at the poi hen the valu

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Q: Choose the gradient of the function f defined by f(x,v,z) = cos(xy +9xz + 13yz). O sin(xy O -cos(…

A: Take gradient and solve

Q: Let z = f(x, y) = x² + y² be the temperature at a point (x, y) = R². (a) Draw a sketch indicating…

A: We know that the directional derivative of a function z=fx,y at a,b in a direction v→ is calculated…

Q: Consider the function f : R³ R defined by f(x, y, z) = tanh(5x² + 2y² − 3z²) and the point P : (x,…

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Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: Let g(x, y, z) = sin(xyz). (a) Compute the gradient Vg(1, 0, π/2). (b) Compute the directional…

A: As per our guideline, we are supposed to solve only first three subpart. Kindly repost other subpart…

Q: Find the gradient of f(x, y) =x2-5xy+y2 at the point (0, 1)

A: Gradient of the f(x,y) at a point (a,b) is given by :∇f=dfdx(a,b)i+dfdy(a,b)j

Q: Consider the following vector-valued function: y : (−π,0) × (−1,1) → R³, y(u, v) = {cosh (v) cos(u),…

A: Consider the given function  defined as follows..We need to sketch the full image of .

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

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Q: Calculus of vector-valued functions: Calculate each of the following. d (r(t)), where r(t) = 3 cos²…

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Q: 1. Find the gradient of f(x, y, z) = e2* (sin a – cos y).

A: Gradient of functions

Q: a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf…

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