let U and y be bounded sets. if u er i tre M+ (V) ≤M₂ (V) and M^ (U) SM³ (V) 1

Q: 6. f(x, y) = (x - 1)² + (x −y)¹. − Ans.: global minimum 0 at (1,1).

A: Given function is f(x, y) = (x-1)4 + (x-y)4

Q: If ƒx(a, b) = ƒy(a, b) = 0, does it follow that ƒ has a local maximum or local minimum at (a, b)?…

A: To determine: Whether the function f follows that it has a local maximum or local minimum at a point…

Q: az əz If z= f(x,y), where x = (s+1) , y = (s- t). Then Əs at

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Q: Suppose g(x,y)=x^3−12xy+6y^2 In each case give all three coordinates of each point: (a,b,c). 1.…

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Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

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Q: Find the absolute minimum and absolute maximum of the function f(x, y) = x^3 – 2y^3 + 3y + (x – 1)^2…

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Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: find where itin creasing awd deveas ihng also fî hl the alobal maximum and minimam. himan f…

A: Topic- application of derivatives

Q: 4 Suppose that f(x, y) = x4 + y xy

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Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

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Q: Let f be a function of two variables such that Vf(x, y) and f(2,1) 4 = af • If, in addition, x =…

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Q: Determine the minimum and maximum values ​​of f(x, y, z) = x^2 +2y^2+ 3z^2 subject to restrictions…

A: Given function is fx,y,z=x2+2y2+3z2 subject to  x+y+z=1x-y+2z=2 Let  gx,y,z=x+y+z-1hx,y,z=x-y+2z-2…

Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x4 + y4 − 4xy + 6, D =…

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Q: 3. Let z = yg(x2 - y²) be a differentiable function. Show that z(x,y) satisfies 1 дz 10z 7 - + - = х…

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Q: Suppose that f(x, y) 3x + 3y* 2xy Then the minimum value of f is

A: We have to solve given problem:

Q: Determine the maximum r-values of r-7cos4e. 8- 0. * 3x 3x e= 0, e= 0, .

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Q: Determine the set of points at which the function is continuous. if (x, y) # (0, 0) 5x? + y? f(x, y)…

A: We know that given function is continuous in its domain so we need to check only at point where…

Q: Find the absolute maximum and minimum values of f on the set D. f(x,y) = xy2 + 9 D = {(x,y)|  x >…

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Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Please take turns to work on the following questions: 1. Let f(x, y) = x² + 3xy + y² Compute (a) af…

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Q: *י 4** *)א hauoded

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Q: ind the absolute maximum and minimum values of f(x,y) = {(x, y) : y ≥ x², y ≤ 4}. = 3x² + 2y² - 4y…

A: Solution :  To find the absolute maximum and minimum values of f(x, y) = 3x ^ 2 + 2y ^ 2 - 4y on the…

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: Let T : R^2 → R^3 be a linear map. What are the possibilities for the pair of numbers (dim Null…

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