Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0) and (1,2) with positive orientation.

Q: let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the…

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Q: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Calculate the directional derivative of the function f(x, y, z) = 2x³y − ln(y)x²z − z² at the…

A: Answer

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Calculate the directional derivative of g(r, y, z) = 4 In(r + e2) at (0, 1, 0) in the direction from…

A: For directional derivative let us first compute derivatives

Q: Determine the directional derivative of the function f (x, y, z) = x2 + xy + y + z2 in point P = (1;…

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Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

Q: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

A: Given function is f(z)=z*2z, z>00,        z=0 we have to prove, the above function is not…

Q: ind the directional derivative of the function f(x, y, z) = Vx² + y² + z² at point (2, -3, 6) in the…

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Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: 12. Find the directional derivative of f(x, y, z)=zy+yz+xzat (1, 1, 2) in the direction of u =…

A: We can find the directional derivative in the following steps.

Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

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: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

A: Solution a: Given function is f(x, y)=xy+y Now gradient of the function is ∆f(x, y)=∂f∂x, ∂f∂y⇒∆f(x,…

Q: Consider the function 422 + Vy+3z . f(x, y, z) = 3x – 7 Find the directional derivative of f at the…

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Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

Q: Let f(x, y, z) = x In y - exz.Calculate the directional derivative of fat point (-5, 1, -2) and…

A: In this question, we find the directional derivative of the function f(x,y,z)=xln(y)-exz3The line…

Q: Q3] Let f(x, y, z) = x In y- e.Cakulate the directional derivative of fat point (-5, 1, -2) and…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: 3. Find the directional derivative of f(x, y, z) =x*y-yz' +z at the point (1, -2,0) in the direction…

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Q: =) Find the directional derivative at the point P = (2, 1, 1) of the scalar function in the…

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Q: Find the directional derivative of the function f(x, Y, z) = x + ln(y² + z²) at the point A(2,1, 1)…

A: To find the directional derivative of the function f(x,y,z)=x+ln(y2+z2) at point A(2,1,1)  in the…

Q: Compute the directional derivative of the function f(x,y, z) = 3ryz at the point P: (1, –3, –1) in…

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Q: Compute the directional derivative of the function f(x, y, z) = 3xyz at the point P = (1, −3, −1) in…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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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: #1. Find the directional derivative of the function f(x,y,z) = x²y + 2y2z at the point (1,–2,0) in…

A: Given:

Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: Let F(x, y) = [2ry² +x, 2r²y + y]. Find all functions f with gradient F. Find the derivative of f in…

A: # we are entitled to solve 3 subparts at a time ,please resubmit the other subparts if you wish to…

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

Q: Let f(x, y, z) = 3xy + 2yz - xz. Find the directional derivative of f(x, y, z) in the direction of…

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

A: The directinal derivative is given below

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector <p, q, r> can be…

Q: 8. Let f (x, Y, z) = ln (x² + y² – 1) + y + 6z. In what direction ī is f(x,y, z) increasing most…

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

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

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Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function f(x, y, z)=(x3-xy2-z).........(1) We have to find the derivative of the function…

Q: (2) This exercise is to convince the student that the extension of the differentiation rules from…

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

A: Given: Function f(x, y, z) = x2y + y2z , point (1, 5, 6) and vector v = <2, -1, 2> To Find:…

Q: Let if (x, y, z) # (0,0, 0) if (x, y, z) = (0, 0, 0) xyz x²+y²+z² > f(x, y, z) = { 10, (a) Use the…

A: fx, y , z = xyzx2 + y2 + z2, if (x, y , z) ≠(0,0,0)                             0,…