Find a formula for the distance from the point P{x,y,z) to each of the following planes....
Use the gradient rules to find the gradient of the given function, f(x,y,z) = x+yz y+xz Choose the correct answer below. 1 O A. Vf(x,y,z) = -((1-z?)z(z2 - 1).y? - x?) (y + xz)? OB. Vf(x,y,z) = (z(1-z?)y(z? - 1),z2 + x2) (x + yz)? O c. Vf(x,y,z) = (y(1+z2),x(z? + 1).y? - z?) (x + yz)? OD. Vf(x,y,z) = -(y (1-2²), x(2² - 1), y² - x²) (y + xz)2
The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c In To 2 + y2 where c> 0 is a constant and ro is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. a. Find the components of the electric field in the x- and y-directions, where E(x,y)= - VV(x,y). Choose...
11.1.37 Describe the given set with a single equation or with a pair of equations. The plane through the point (9.4.-6) parallel to a. the xy-plane b. the yz-plane c. the xz-plane a. Choose the correct equation of a plane parallel to the xy-plane. O A. y = 4 OB. z= -6 O c. x=9
Given the function 1 f(x,y) = answer the following questions. 36 - 16x2 - 16y2 a. Find the function's domain. b. Find the function's range. c. Describe the function's level curves. d. Find the boundary of the function's domain. e. Determine if the domain is an open region, a closed region, both, or neither. f. Decide if the domain is bounded or unbounded. a. Choose the correct domain. OA. 9 The set of all points in the xy-plane that satisfy...
(8) The Divergence Theorem for Flux in Space F(x, y, z) =< P, Q, R >=< xz, yz, 222 > S: Bounded by z = 4 – x² - y2 and z = 0 Flux =S} F înds S (8a) Find the Flux of the vector field F through this closed surface. (8) The Divergence Theorem for Flux in Space F(x,y,z) =< P,Q,R >=< xz, yz, 222 > S: Bounded by z = 4 – x2 - y2 and z...
F(x,y,z) =< P, Q, R >=< xz, yz, 2z2 > S: Bounded by z = 1 – x2 - y2 and z = 0) Flux =SS F ñds S (8a) Find the Flux of the vector field F through this closed surface.
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
Find the shortest distance from the point P(2,3,0) to the plane 5x +y + z =1 and the corrdinates of the point Q on the plane that is closest to the point P(2,3,0)
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...
(1 point) Find the maximum and minimum values of the function f(x, y, z) = yz + xy subject to the constraints y2 + z2 Minimum value is | = 196 and xy = 8. Maximum value is