(4) For the f(z) given in parts (a) and (b) below determine for what values of...
Given f : R → R4, f(x, y, z) = (x2 + y2, 2, x + 2, y2 + x3) (Hint: f is not linear) (a) (1 point) Find the kernel of f. (b) (1 point) Find the range of f. (c) (1 point) Is f is 1-1? Is f onto? Justify your answers.
1. Write f(z) in the form f(x) = u(x, y) +iv(x, y). (a) f(x) = 23+2+1 (b) f(3) = 2,270. Suppose f(z) = x2 - y2 - 2y +i (2x - 2xy), where z = x + iy, and express () in terms of .
Use Lagrange multiplier to determine the maximum and minimum values of (f,x,y,z) = x^2 +y^2 +z^2 subject to xyz=4 Detailed solution please. Thank you! 20. Use Lagrange Multiplier to determine the maximum and minimum values of f(x, y, z)-x2 + y2 +12 subject to 20. Use Lagrange Multiplier to determine the maximum and minimum values of f(x, y, z)-x2 + y2 +12 subject to
8. Determine whether the following functions reach a maximum or minimum and the values of x and y for a maximum or minimum. a) Z(x, y) = x2 + 3y2 - 3xy b) W(x, y, z) = 29-(x2 + y2 + 22)
#10 and #12 8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possible relativema imun or minimum value 10. Both first partial derivatives of f(x.y)-x-4xyy are zero at the points (0 11. Find all points (x,y) where f(e.y) 2x2+3xy + 5y has possible relative maximum or minimum values. Then, use the 12. Use the second...
5 Use the Divergence theorem to find the outward flux. a. F(a, y,z)-(6x2+ + 2xy, 2y + xz, 4x2y); G: The solid cut from the first octant by the cylinder x2+y - 4 and the plane 3. (In(x2+Уг),-2z arctan(y/x), z (x2 +y2); G:The solid between the b. F(r, y, z) Vx + y*); G: The solid between the cylinders x2 + y.2 1 and x2+ y2 2, -1szs4. c Fxy)-(2xy', 2x'y, -): G: The solid bounded by the cylinder x?1...
All parts please. Negative Leading Coefficient 1. Use the graph of f'(x) to answer: On which interval is f(x) increasing? Even Degree Justify your answer. 28+ -50+ -1 F(x) - O 2. Given the table and information below, complete the table to describe the behavior of f(x) and justify your conclusions with reference to the derivative. Sketch a possible graph for f(x) that goes through the point (-1,4) F"(x) Fis: F is: 3. Sketch a possible graph for f(x) that...
Can i have this as soon as possible please? I will give a rate!! or f(x, y, z) x2y + y2 + xz , compute a) the directional derivative at ( 1, 2, 4) in the direction of 12,2,1) , b) the maximum value of the directional derivative of fat (1.2,4), and c) the direction of the minimum directional derivative of fat (1,2,4). (10 pts) or f(x, y, z) x2y + y2 + xz , compute a) the directional derivative...
Please help solve the following with steps. Thank you! 3. Determine the center of mass of the paraboloid given by the surface -4-x2-y2 and (a) ρ(x, y, z)= 1 (b) pr, y,a) 5 0 if -z 3. Determine the center of mass of the paraboloid given by the surface -4-x2-y2 and (a) ρ(x, y, z)= 1 (b) pr, y,a) 5 0 if -z
[3](4 pts) Let f(x) = u(x, y) + iv(x,y) be differentiable for all z = x + iy. If v(x, y) = x + xy + y2 – x2, for all (x, y), find u(x,y) and express f(x) explicitly in terms of z.