Setup triple integrals of f(x,y,z) in sepherical coordinates for each of the regions below.
The region to the left (-y direction) of
and the right (+y direction) of
that is not contained in the first or fourth octant.
Setup triple integrals of f(x,y,z) in sepherical coordinates for each of the regions below. The r...
Use the triple integrals and spherical coordinates to find the volume of the solid that is bounded by the graphs of the given equations. x^2+y^2=4, y=x, y=sqrt(3)x, z=0, in first octant.
4. Let E be the region in the first octant of R3 contained in the sphere. (a) Formulate the triple integral JJ JBzdV JJJE zdrdydz in spheri iterated integrals ca coordinates as three hi Formulate the triple integral in cylindrical coordinates as three iterated integrals c) Formulate the triple integral in Cartesian coordinates as three iterated integrals
4. Let E be the region in the first octant of R3 contained in the sphere. (a) Formulate the triple integral JJ JBzdV...
Question 7 5 pts each Write iterated integrals for each of the given calu lations. Do not evaluate. (A) The integral of f(x, )212y over the domain D: 2 y 20. (B) The integral of f(x, y, z) = 12x + 3 over the volume contained in the first octant and below the graph z 8-y 2 (C) The mass of an object occupying the region bounded between the sur faces x2 + y2 + Z2 = 16 and z...
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
Use spherical coordinates to calculate the triple integral of f(x, y, z) over the given region. f(x, y, z) = y; x2 + y2 + 22 < 25, x, y, z<o 6251 6251
You only have to set up the integrals on this page. Choose two of the three. The third may be done for bonus. Draw the shadow for rectangular and cylindrical. 6. Use rectangular coordinates and triple integrals to get the volume of the region E in the first octant (x,y,z > 0) below the plane 6x + 3y +z = 12 E 1 26.0,12) *x+3y+z=12 You,o) Y (1,0,0)
/// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z
/// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z
5. Express the triple integral | f(x,y,z)dV as an iterated integral in cartesian coordinates. E is the region inside the sphere x2 + y2 + z2 = 2 and above the elliptic paraboloid z = x2 + y2
Find the extreme values of subject to constraints and . f(x, y, z) y+ z = 2 We were unable to transcribe this image f(x, y, z) y+ z = 2
Find an equation of the tangent plane to the surface f (x, y) =
x tan y at the point (2,
/4, 2).
a. x - 4y - z =
b. None of these
c. x + 4y - z = -
d. -x + 4y - z =
e. - x + 4y - z =
/4
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