2. Let f(x, y) = |xl + lyl. Determine the equations and shapes of the cross-sections when x 0, y ...
let f(x,y)=sqrt(49-x^2-y^2) (A) describe the cross sections of the surface Z=f(x,y) produced by cutting it with the planes y=1, y=3, and y=5. (B) describe the cross sections of the surface in the planes x=1, x=3, and x=5. (C) describe the surface z=f(x,y). Let f(x,y) = 49 - x? -y?. (A) Describe the cross sections of the surface z=f(xy) produced by cutting it with the planes y = 1, y = 3, and y-5, (B) Describe the cross sections of the...
Consider the function f (x, y)=6-32 -32 (a) Determine the level curves for the surface when z 0,3, 6. Sketch these three level curves in the ry plane. (b) Determine the cross-sectional curves of the surface in the rz plane and in the yz plane. Sketch these two cross-sectional curves. (c) Sketch the surface z f(x, y) (d) What is the maximal domain and range of f? (e) Evaluate the double integral f(ar, y) da dy Consider the function f...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
2. (20pt.) Let f(x, y) 2 (a) draw and describe the level curves of f of value c= 0,1,2,4 (b) sketch the graph of f (r.y) 2. (20pt.) Let f(x, y) 2 (a) draw and describe the level curves of f of value c= 0,1,2,4 (b) sketch the graph of f (r.y)
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface. 2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
Exercise 6.B.3. Let the pair of random variables (X, Y) have joint density function f(x, y)-16(x-y)2 įf x, y e [0, 11, 0 otherwise. a. Confirm that f is a joint density function by verifying that equation (6.B.4) holds, and use a computer or graphing calculator to sketch its graph. b. Compute the marginal density function of Y c. For each x e [0,1], compute the conditional density of Y given x. d. Compute the conditional expectation function E(Y|X =...
3. (50 pts) Let (X,Y) have joint pdf given by -{ c, lyl< x, 0 < x < 1, f(x,y) = 0, 0.w., (a) Find the constant c. (b) Find fx(x) and fy(y) (c) For 0< x<1, find fy x-() and pyix- and ox (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
ry 82. Let f(x, y) - 0 if (x, y)-0 The graph of f is shown on page 813. a. Show that j x,0) - x for all x, and a0, y) y for all y. b. Show that (0, 0) ахау (0, 0) The three-dimensional Laplace equation dy dx is satisfied by steady-state temperature distributions T-f(x, y, z) in space, by gravitational potentials, and by electrostatic poten- tials. The two-dimensional Laplace equation ar'ду obtained by dropping the a2f/az2 term...
Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t...
Let f(0, -2) = 4 and 0f (0, -2) = 6,23). a. Write the parametric equations of the line in the xy-plane that is perpendicular to the contour f(x,y) = 4 at ( 0-2). b. Write an equation for the tangent plane to the surface z = f(x,y) at (0, -2,4).