2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and 2. Find the average value of the function f(x,y) y 2. (Sketch the region.)...
Find the global maximum of 2 = f(x,y) = 3y - xy over the region bounded by y=x², y = 0, and x = 4.
please answer question 3. 1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
Find the average value of f(x, y) over the region Rwhere A is the area of R in the following equation. Average value - Ā J 1(x,y) dA f(x,y) = xy R: rectangle with vertices (0, 0), (7,0), (1, 2), (0, 2) Enter a number Submit Answer Practice Another Version
1. Sketch the region bounded by the graph of y = – and the x-axis over the interval [1, 3) and then find the area of the region. (10 points)
Find the average value of the function f over the given region. f(x,y) = 8x + 10y over the triangle with vertices (0,0). (10,0), and (0.6). O A. 30 OB. 80 3 OC. 140 3 OD. 86 3
Find the average value of the function over the given solid. The average value of a continuous function f(x, y, z) over a solid region Q is 11 f(x, y, z) DV where V is the volume of the solid region Q. f(x, y, z) = xyz over the cube in the first octant bounded by the coordinate planes and the planes x = 16, y = 16, and z = 16.
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...
xy=1 and y 2x V -X -Region S is bounded by the lines xy 2. Draw the region and indicate all the vertices. and the hyperbolas 2 and B) Transfer region S from x-y to u-v plane and indicate all the vertices on the new plane acx. y au,v) =1 C) Show that the area corrections are related by (u,v) x, y) D) Find the centroid of region S xy=1 and y 2x V -X -Region S is bounded by...
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the region R (label lines, intercepts, axes and shade region) (b) SET UP the integral over this region (c) Assuming f(x.y)- xa is the density function for the lamina R given above, determine the mass for R 5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2) Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...