4. Determine u(z,y) and v(x, y) from the function f(z)=ze²

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

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Q: Compute the gradient of the function at the given point. f(x, y) = 10x - 8y, (10,8)

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Q: Find fyx. zyx 5,6 3 f(x, y, z) = x³y2³ + xy + yºz z

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Q: ye-(²²+y²+z²). Find all points (x, y, z) such that Vf(x, Y, z) = Question 2. Consider the function…

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

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Q: Let v = (2, (2, 3, 2) 3,

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Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Graph and shade the domain of f(x, y) = vy + x² – 2.

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Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A: Given: Fx,y,z=xy j+6xyz k To find the  cross product of ∇×∇×F

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Find the gradient of f(r, y, z) = xy?z³ + In(ryz) at the point (1, 1, 1).

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Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: Compute Fx, fy, and fz for the function and evaluate them at the indicated points

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Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Consider f(x,y) = xe*y +. Find fx , fy and fxy. y

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: Find the linearization of the function f(p, q) = Pat (0,0) p-1 q+1

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Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z + z.x] at the point 1-z…

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Q: 3. Which of the following represent linear function? a) 3x = 20-4y b) y-4 =0 c) x' +3y = -10 d) y =…

A: The function which can be expressed in the form of Y=aX+b is called as a linear function.

Q: y = Arccot (cosx ) ; y' ' O sin x/ (1+ sin*2 (x) ) ) - sin x / (1+ sin^2 (x) ) ) sin x/ sqrt (1-…

A: Given y=cot-1cosx We will find y'that is the derivative of y. Chain Rule: If y=fgx, then y'=f'gx·g'x