Evaluate f(x, y, z) dV for the function f and region W specified. f(x, y, z)...
Evaluate \(\iiint_{\mathcal{B}} f(x, y, z) d V\) for the specified function \(f\) and \(\mathcal{B}\) :$$ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 16,0 \leq y \leq 5,0 \leq z \leq 2 $$\(\iiint_{\mathcal{B}} f(x, y, z) d V=\)
Consider the function f and region E. f(x, y, z) = y, E = {(x, y, z)| 1 5 x2 +3? 59,0 SyS 1 - x2 - 22; (a) Express the region E in cylindrical coordinates. O E = {(r, 0, 2)Iisrs9,0 SO S 21,0 S 231-23 O E = {(1, 0, 2)| 1 575 3,0 SOST,O SZS 1-12} O E = {(r, 0, 2)Ii Srs 3,0 s E s 2,0 S 25 1 - 2 O E = {(r,...
Question3: Evaluate SSE (x - y)dv, where E is the region enclosed by z= x2 – 1, z = 1 - x2, y = 0, and y = 2.
(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y, z) |2 < x < 4,0 Sy < 3,15 zse}. 2 Evaluate | $180,0,.2) av. R
The average value of a function f(x, y, z) over a solid region E is defined to be fave = V(E) f(x, y, z) dv where V(E) is the volume of E. For instance, if p is a density function, then Pave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 9 – x2 - y2 and the plane z...
12xz dV, where S is the solid region in the first octant (x, y, z > 0) that lies above the parabolic cylinder z = y2 and below the paraboloid Evaluate the triple integral I = 1] 1222 dV, where S ist 2= 8 – 2x2 - y2.
Evaluate SIS 2xz dV where E = {(x, y, z) | 0 < x < 2, x < y < 2x, 0 < z < x + 3y}
(1 point) Write limits of integration for the integral Sw f(x, y, z) dV, where W is the quarter cylinder shown, if the length of the cylinder is 3 and its radius is 2. Z Sw f(x,y,z) dV = SSS f(z,y,z)d d d where a = b= I d= and f (Note: values for all answer blanks must be supplied for this problem to be able to check the answers provided.)
8. Evaluate the triple integral of the function f(x, y, z) = 6x over the solid region E that lies below the plane r+y - 2 = -1 and above the region in the ry plane bounded by the Vy, y = 1, and r=0. curves =
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...