Find the extremum of F (x, y) = x ^ 2 + y ^ 2 + XY under the condition of X + 2Y = 4

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• 1. Let z = XF (XY ^ 2, e ^ (the square of x) multiply y), F have continuous partial derivatives, find ZX, ZY
• 2. Solve the equations XY + XZ = 8-x ^ 2, YX + YZ = 12-y ^ 2, ZY + ZX = - 4-z ^ 2 Solve the equations XY + XZ = 8-x ^ 2, YX + YZ = 12-y ^ 2, ZY + ZX = - 4-z ^ 2
• 3. Given the vector a = (- 2,3), B = (1, - 2), then their scalar product a * b =?
• 4. If a and B are known to be real numbers, what is the condition that "a power of 2 > B power of 2" is "LNA > LNB"
• 5. Set a = {(x, y) y = x & # 178; + MX + 2}, set B = {(x, y) X-Y + 1 = 0,0 ≤ x ≤ 2}, if a ∩ B ≠ & # 8709;, find the value range of real number K
• 6. How to find the plane normal vector, please explain the specific method!
• 7. Given that the vector M = (3,4) the vector m-the absolute value of the vector n = 1, then the value range of the absolute value of the vector n
• 8. Blank space to answer 1. Change the quadratic function y = - 2x2 (quadratic) + 4x + 3 to y = a (x + m) 2 + K 2. Quadratic function y = X2 (quadratic) + X-5 when the minimum value of independent variable x =, y is 3. It is known that the image of the quadratic function y = (m-2) X2 (quadratic) + M2 (quadratic, not explained) - m-2 of X passes through the origin, then M =. At that time, y increases with the increase of X 4. For the image of y = 2 (x-3) 2 + 2, the following statement is correct () A. The mark of fixed point is (- 3,2) B. the axis of symmetry is y = 3 C. When x is greater than or equal to 3, y increases with the increase of X. when x is greater than or equal to 3, y decreases with the increase of X 5. In the same coordinate system, make the image of y = 2x2 + 2, y = - 2x2-1, y = half X2, then they () A. It's all about the y-axis symmetry B. the vertices are all at the origin C. they're all parabolas, opening up D. they're all wrong 6. It is known that the intersection of a parabola and x-axis is a (- 2,0), B (1,0), and passes through point C (2,8) (1) Find the analytic formula of the parabola. (2) find the vertex coordinates of the parabola
• 9. It is known that the value of X which makes the derivative of the function y = X3 + ax2-43a 0 also makes the value of y 0, then the value of constant a is () A. 0b. ± 3C. 0 or ± 3D
• 10. X + y = XY, x = 0, y = 0... X = 2, y = 2... We also need a set of
• 11. It is known that f (x) is a function defined on R which is not always zero, and f (x) satisfies f (XY) = YF (x) + XF (y) for any x, y in the domain of definition (1) Find the value of F (1), f (- 1) (2) Judge the parity of F (x) white and explain the reason
• 12. It is known that f (x) is defined on R and is not equal to 0. For any x, y ∈ R, f (XY) = XF (y) + YF (x) 1. Find the values of F (0), f (1), f (- 1) 2. Judge the parity of F (x) and prove it
• 13. It is known that f (x) is a function defined on R which is not always zero. For any x, y ∈ R, f (x · y) = XF (y) + YF (x) holds. & nbsp; sequence {an} satisfies an = f (2n) (n ∈ n *), and A1 = 2. Then the general term formula of sequence an=______ ．
• 14. It is known that f (x) is a function defined on R which is not always zero, and for any x, y ∈ R, f (XY) = XF (y) + YF (x) The problem is if y = f (x) is an increasing function on [0, + ∞) and satisfies f (x) + F (x-1 / 2)
• 15. We know that the function f (x) defined on the real number set is not always 0, and for any X. y belongs to R, satisfying XF (y) = YF (x), and judge the parity of F (x)
• 16. Finding the second order partial derivative of Z = XY + (x ^ 2) siny
• 17. Finding the partial derivative of SiNx * e ^ XY
• 18. Z = arcsin (XY) to find the second derivative of this function There are four answers, two of which are equal
• 19. The partial derivative d ^ Z / DXDY of Z = f (XY, y)
• 20. Let z = (x, y) be a function determined by F (X-Y, Y-Z, z-x) = 0, and let F 2 'not equal to f 3', try to find the partial derivative ᦉ 8706; Z / ᦉ 8706; X, ᦉ 8706; Z / ᦉ 8706; y