8. Find the surface area of the part of the plane z+y+z4 over the rectangle [0, 1]x[0,2 b) 3 c) 2...
Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface area - f(x, y) ds z =f(x, y) Lateral surface xy) As C: Curve in xy-plane Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface...
Find the area of the surface. The part of the plane z = 6 + 2x + 3y that lies above the rectangle (0, 9] [1, 6]
Find the area of the portion of the plane 2x+3y+4z=28 lying above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane. (1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22 < 36 Area(S)- (1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22
Let D be a region in the (x, y)-plane. If a, b,c >0, let Sa be the part of the hyperbolic paraboloid z = axy in R3 with (x,y) E D, and let Tổ.c be the part of the elliptic paraboloid·bz2 + суг in R3 with (x,y) D. For a given a > 0, find b,c >0 such that Tb,e has the same area as Sa Let D be a region in the (x, y)-plane. If a, b,c >0, let...
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29 8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
3 Calculate the following surface integral (1 7.ds over the surface x² + y +z =1 , x 20,42 0,2 2 0 where 5 = [x,y,z] . 10 . 5 00
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = x2 + y2, R = {(x, y): 0 = f(x,y) 3}
2. (a) Find the area of the region bounded by the parabolas y 6z - 2 and y 22 (b) (Optional) Find the area of the region between the curves y2 and y - 22".. over the interval [0,2. 2 36 3. (Review) Evaluate the limit lim 4. (Review) A rectangle has its base on the z-axis and its two upper vertices on the curve y 5-x4. What is the largest area the rectangle can have? 2. (a) Find the...