Find the volume inside both x^2+y^2+z^2=1 and x^2+y^2=x.
Find the volume inside both x^2+y^2+z^2=1 and x^2+y^2=x. Q4 (10 points) Find the volume inside both...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
show all steps = 1 and Find the volume inside both x2 + y2 + z2 x2 + y2 = x.
Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 - 16 and (x - 2)2 + y2-4 Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 - 16 and (x - 2)2 + y2-4
orientation. Find the volume of the piece of the sphere x2 + y2 + z2-1 which lies both inside the cylinder x2 + y2-1/2 and inside the first coordinate octant (that is, x,y,z 2 0). 4. 5. For the vector field F (2x(y +2)-y2-Z2), what is the surface integral of this field over the unit-radius
(9 points) Suppose f(x, y, z) = - and D is the domain inside the sphere x2 + y2 + z2 x2 + y2 + z2 = 1 and outside the cone za Enter p as rho, as phi, and as theta. As an iterated integral, BRD (F sav = SITE dp do do JA JC JE with limits of integration
Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the hemisphere z 16-x-yi and outside the cylinder x2 + y2 = a 2 is one-half the volume of the hemisphere. Do not solve it. Problem 6 [5 points] |(y ( y-dan- 0.708 Set up an equation with a double Integral in polar coordinates to find a such that the volume inside the...
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
aw au B. Find the points in which the line x = 1 + 2t, y = -1 – t, z = 3t, meets the three coordinate planes. C. Evaluate and at the given point. w = In (x2 + y2+ z2), x = ue") y = ue'sinu, z = uecosu, (u, v) = (-2,0) A. Find the volume of the solid. II. z = 4 - 4(x2 + y2) z = (x2 + y2)2 - 1
10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y plane, oriented counter-clockwise. Find Jscurl(F) ndS directly and by using Stokes' Theorem. , where S is the up 10. Let F(x, y, z) = 〈y,-z, 10) per half of x2 +y2 + z2 = 1, oriented upward, and C the circle 2 y 1 in the z - y...
10. Consider the integral (x + y + z) dV where D is the volume inside the sphere x2 + y2 + x2 = 9 and above the plane z = 1. (a) (3 marks) Express I as an iterated integral using Cartesian coordinates with the order of integration z, x and y. DO NOT EVALUATE THIS INTEGRAL. (b) (3 marks) Express I as an iterated integral using spherical coordinates with the order of integration p, 0, and 0. DO...