Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces....
2.31 solution Section 2.5-Constant-Coordinate Surfaces 2.31 Describe the intersection of the following surfaces: (a) * = 2, y = 5 (b) x = 2, y = -1, z = 10 (c) r = 10, 0 = 30° (d) p = 5, 6 = 40° (e) $ = 60°, z = 10 (f) r = 5, 0 = 90°
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
all have same options please only answer if you're 100% sure what do the level surfaces of rx, y, z) = 9x2-9y2 + 9z2 look like? [Hint: Use cross-sections with y constant instead of cross-sections with z constant.] For f(x, y, z) > 0, the level surface is a Select- Select- . For f(x, y, z) < 0, the level surface is a For f(x, y, z)-0, the level surface is a hyperboloid of one sheet X cone hyperboloid of...
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
Parameterize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parameterization of its boundary, 6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
11. Point P(4,2,3) is on one of the level surfaces of g(x, y, z) = e*+4xy”. Write an equation of the plane tangent to this surface at point P. a)5(x-4) - 7(y-2) + 6(2-3) = 0 b)-8(x-4)+12(y-2) - 5(2-3) = 0 c)9(x-4) + 4(y-2) - 5(2-3) - 0 d)16(x-4) + 64(y-2)+(2-3) -0 e) none of these
partial differential equations question Problem 6. a) Find all possible surfaces orthogonal to the planes x + 2y + cz = 1, where c is an arbitrary real constant. (b) Find the surface orthogonal to the planes x+2y+cz = 1 passing through the curve I: x = s, y = s, z = sa.
Write a logarithmic equation corresponding to the graph shown. Use f(x) = log (x) as the parent function. y = X y 8 6 4 NO x -8 -6 - 4 -2 2 4 6 8 (-2, -3) -6 Note that the equation of the given graph will be of the form f(x) = a logo function y = logb(x), and compare the x-intercepts and vertical asymptote identifiable intentheah halte determine the constanta
Problem 4 a5 pts) La f(x,y,z) = 3x2+2+2 (a) Draw a few of the level surfaces (4.3.2) = c for admissible values of cand classify the type of surface these are (b) Compute the directional derivative of fat (1.2.3) in the direction of the vector û= 2.2.1). (c) Find the value and direction of the maximum rate of change off at the point(1.2.3).
4 points) Write the equation in the form y-f(u/z) then use the substitution y zu to find an implicit general solution. Then solve the initial value problem. The resulting differential equation in z and u can be written as zu' Separating variables we arrive at Separating variables and and simplifying the solution can be written in the form u2 1-Cf(x) where C is an arbitrary constant and which is separable. da du f(x) ias problem is