1. Prove that the following functions are quasi-concave: (i) f(x, y) = ryt, r > 0, y > 0; e-24, x > 0. (ii) f(x, y) =

Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: 2 Let f(x,y) = x +y ². Which of the following is the minimum directional derivative of the function…

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Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: Let F(x, y, z) y³ 2:5 . What is the value of div F at (1, 2, 3)?

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Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Consider the function. f(x, y) = 2(y + 1)x² Identify the point(s) on the graph of f at which the…

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Q: Find the Green's function for the Helmholtz equation (V2+k²)u = 0 in the interior of the unit square…

A: Given the equation                       ∇2+k2u=0, in the interior of the unit square 0≤x, y≤1, with…

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: 3. Find the derivative of the function f(x, y, z) = xy + yz + zx at the point (1,-1, 2) in the…

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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