A force field (in newtons) is defined by F(x, y) = [ + + x, 1 x² +1 y³ зав where coordinates x and y are in meters. (a) Evaluate F(0, 1), F(1, 1), F(-1, -1), F(2, -1) and sketch them on the xy-plane.

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: Let f(x, y) = x² + 5y². (a) Find f (5, 1) and f,(5, 1). fx(5, 1) fy(5, 1) =

A: Find

Q: 3.1 (x+1) (x'+5x+2) ふeren ta ee

A: Topic = Derivative As per guidelines , At a time only one question can be answered.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

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Q: If A = yz(^2) i - 3xz(^2) j + 2xyz k , B = 3x i + 4z j - xy k and ∅= xyz , find (a) Ax (∇∅), (b)…

A: Since you posted a question with multiple sub-parts, we will solve first three sub-parts for you. To…

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

A:

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Given f(x, y) = 4/32° + y + 8xy³, find f.(x, y) = f,(x, y) = |

A: Find the partial derivative of f(x,y) with respect to x to find fx(x,y) . Find the partial…