f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves...
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...
4. (8 pts.) The level curves of z = = f (x, y) are given along with the constraint curve g(x, y)= 8 9(x, y) = 8 40 50 60 70 0 30 20 10 a. Maximize and minimize f on the constraint. b. Label the point where the maximum occurs as A and the point where the minimum occurs as B. c. Sketch in the approximate vectors Vf and Vg at the points A and B.
39. Let L be the minimum length of a ladder that can reach over a fence of height h to a wall located a distance b behind the wall. a. Use Lagrange multipliers to show that L = (h2/3 + 62/3;3/2 (Eigure 20). Hint: Show that the problem amounts to minimizing f (x, y) = (x + b)² + (y+h)? subject to y/b = h/x or ry = bh. b. Show that the value of L is also equal to...
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK YOU SO MUCH J-2 J-V4-z² Ji 26. Let be the region below the paraboloid x2 + y? = z – 2 %3D that lies above the part of the plane * + Y + z = I in the first octant. Express f (x, y, z) dV as an iterated integral (for an arbitrary function J). 27. Assume J (ª, Y, 2) can be expressed as a product, f (x, y, z)...
(This type of math is Multivariable Calculus 1) 7. Sketch the level curves of f(x, y) = p 16 − x 2 − y 2 for levels c = 0, 1, 2, 3, 4. Can you describe the surface? 17. An ideal fluid flow is modeled with the velocity potential ϕ = 4x−3y and stream function ψ = 3x + 4y. Sketch some streamlines for this flow. Can you describe this flow in a sentence or two?
5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c) Sketch Vf at P and Q on the level curve f(x, y) = 3. 5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c)...
final study guide, please help 1.) Sketch the indicated level curves of the following functions. 0, z = 2, and z = 4 level curves of f(x,y)-хуз. The z =-2, z ). log025 (x + y2 2 level curves of h(x,y) -1,2-0, z-, 1, and z ii. The z ii. The z7, z 4,z 3, z 2, and z1 level curves of g(x.y) +3 1.) Sketch the indicated level curves of the following functions. 0, z = 2, and z...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
7) Given f(x,y)= x^2+y^2+2, subject to the constraint g(x,y)=x^2+xy+y^2-4=0, write the system of equations which must be solved to optimize f using Lagrange Multipliers.
QUESTION 9 Find the domain and range and describe the level curves for the function f(x,y) y+10 1(x, y)s a.Domain: all points in the x-y plane excluding x O: range: all real numbers; level curves: parabolas y ex2-10 b. Domain all points in the xey plane; range: real numbersz 0: level curves: parabolas y- ex2- 10 Domain :all points in the x-y plane; range: all real numbors; levol curvos: parabolas y ex2-10 d. Domain all points in the x-y plane...