Calculus Answers

1.Let f(x)=x+1,g(x)=x^2-3. Solve the following equation for x [(fog)(x)+(gof)(x)=0]
2.Determine whether the following function is invertible or not, if it is , find its inverse,
g(x)=x-1/3x+2

Evaluate the iterated integral ∫(0 to π/3)∫(0 to y)∫(0 to x) cos(x+y+z) dzdxdy.

Evaluate the iterated integral ∫(0 to 1)∫(x to 5x)∫(0 to y) 5xyz dzdydx.

Evaluate ∫∫∫B f(x,y,z) dV for the specified function f and B:

f(x,y,z)=(z/x) 3≤x≤6,0≤y≤4,0≤z≤2

Find the volume of the solid in R^3 bounded by y=x^2, x=y^2, z=x+y+15, and z=0.

Evaluate the triple integral ∭E xy dV where E is the solid tetrahedon with vertices (0,0,0),(2,0,0),(0,10,0),(0,0,1).

Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=25.

Find the centroid (x¯,y¯) of the region bounded by:
y=7x^2+6x, y=0, x=0, and x=6.

Find the mass and center of mass of the cube given by 0≤x≤a, 0≤y≤a, 0≤z≤a for which the density is ρ(x,y,z) =x^2+y^2+z^2.

Evaluate ∬∫D y dV, where the integration volume D is the region bounded by the 3 coordinate planes and 2x+ 2y+z= 4.