Find(dw. and (dw), atte point(w, x, y, z)=(48,3,-2,-2)if w=x2y2 + yz-z3 and x2 +y2 +22 = 17.
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
2 x-I 3. Find the volume of solids enclosed by a paraboloid z x2+ y2 and an x2y2+z2 =6 ellipsoid 4 Sud, a.
pi over 2 is not correct either
Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 2)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 5 that lies above the plane z = 4 and is oriented upward.
22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =
evaluate JJ. (< –Y) A. ) Integrate f(x, y, z) = x2 + y2 + 22 over the cylinder x2 + y2 < 2,-2 <2<3 (IL dx dy dz Feraluate
Find (a) and (), at the point (w, x, y, z)=(14 – 1,1, - 2)if w=2x2y2 +242-222 and x2 + y2 +2=6. ду 2 (Simplify your answer.) (Simplify your answer.)
Prove that the limit does not exist: lim (x,y,z)--> (0,0,0) (xy +yz) / (x2+y2+z2)
Let f(x, y, z) = xeyz – cos(x2 – y2 + 22) a) Find the directional derivative of f at the point (0,0,0) toward the point (1,2,0). b) Find the maximum rate of change of f at point (0,0,0). In which direction does the max rate of change at (0,0,0) does occur? (two questions here!)
Optimize f(x,y,z) = x2+y4+z2 subject to the constraints x3-y2= 1 and z3+x2= 1 Use the second derivative test to try to classify the critical point as a maximum or minimum. Explain why the method of Lagrange multipliers is failing for this example. Use the definition of the derivative to classify the extrema.
x2 + y2 with z 2 0; its (1 point) The region W lies between the spheres x² + y2 + z2 = 4 and x² + y2 + z = 16 and within the cone z = boundary is the closed surface, S, oriented outward. Find the flux of Ě = x; i+y?1+z2k out of S. flux = 5952pi/20(1-1/sqrt2)
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.