8. If f(x, y) = 2x? xy, find f (2,3) and fy (2,3). - 9. If f (x, y) = find f; (1,0) and fy(1,0). 10. If F(x, y) = In(x²y – xy²), find F,(3,2) and F, (3,2). 11. If F(x, y) = e-* tan(x + y), find F(0, n) and F (0,-1). x-y 4

Q: (3) Let 0 = 1234 6789 365 987 in S9 (a) Compute o2 and o (b) Write o as a product of disjoint cycles…

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Q: Find the first partial derivatives of the following function. f(x,y) = /3x + 8xy + 5y²

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Q: Consider the following vector function. r(t) = (2√/2t,6²², 6-2t) (a) Find the unit tangent and unit…

A: Given:  The vector function:  rt = 22t, e2t, e-2t To find: Unit tangent and unit normal vectors.

Q: dz öz Find the partial derivatives, and of the following function: ду ax z = In (2x2 + 4y2)

A: Givenz=ln (2x2+4y2)∂z∂y=∂∂y ln(2x2+4y2)Apply chain rule ∂f∂ygy=f'gyg'yie ln fx'=f'xfx

Q: Find all the second-order partial derivatives of the following function. 2х - 4y x2 + 2y dy?

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Q: q = Ee-EkT; q with respect to T Σ

A: The objective is to find the partial derivative of q=∑e-EikT with respect to T.

Q: Use the duality method to solve each linear programmin 1. Minimize Z = 29x,+ 10x2 subject to: 3x,+…

A: Given that  Minimum z=29x1+10x2subject to 3x1+2x2≥2                   5x1+x2≥3…

Q: 5. z = yex+x Iny xey-y lnx

A: Solution : z=yex+xln(y)xey-yln(x) zx=∂z∂x =∂ ∂ xyex+xlnyxey-ylnx-∂ ∂ xxey-ylnxyex+xlnyxey-ylnx2…

Q: Calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables…

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