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...
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane 5x + y + z = 3Evaluate the triple integral.8z dV, where E is bounded by the cylinder y2 +z2 = 9 and the planes x = 0,y = 3x, and z = 0 in the first octantEUse a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane...
(b). Use the chain rule to find aw and as y = 8 cost, z = s sint when s= 1 and t=0 aw at where w = = 22 + y2 + z2, x = st,
Could you do number 4 please. Thanks 1-8 Evaluate the surface integral s. f(x, y, z) ds Vx2ty2 -vr+) 1. f(x, y, z) Z2; ơ is the portion of the cone z between the planes z 1 and z 2 1 2. f(x, y, z) xy; ơ is the portion of the plane x + y + z lying in the first octant. 3. f(x, y, z) x2y; a is the portion of the cylinder x2z2 1 between the planes...
Provide an appropriate answer. Find aw when u = 3 and v=-7 if w(x, y, z) = xy2,x = 4, y = u + v, and z=u•v. Odw = -4 au 49 56 dw au Odw = -8 au 49 Odw = 24 du 49
4 + x2 + (y-2)2 and the planes z = 1, x =-2, x Find the volume of the solid enclosed by the paraboloid z 2, y 0, and y 4. 4 + x2 + (y-2)2 and the planes z = 1, x =-2, x Find the volume of the solid enclosed by the paraboloid z 2, y 0, and y 4.
aw 4. Find when (r, s) = (1, -1) if w = (2+y+z)?, r=r-s, y = cos(r +s), z = sin(r +s). ar 5. Find the directional derivative of f(x, y, z) = 3x² + yz + 2yz? at P(1,1,1) in a direction normal to the surface x2 – y + z2 = 1.
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 x2 + y2 + z2 = 1 and x2 + y2 = x.
Find the average distance from the origin of all the points of the solid cylinder {(x,y,z) | x2+y2+z2 =<4 and 0=<z=<4}. Use either a triple integral or the formula for the volume of a cylinder, and use either cylindrical or spherical coordinates.
(8 points) Find the points of intersection in R3 of the line L(t) = (3-1, -2+1, 3t) and the unit sphere: x2 + y2 + x2 = 1 (Hint: Use x = 3t - 1, y = -2t + 1 and 2 = 3t in the equation of the sphere, and solve for t.)