## Multivariable Calculus Resources Converting Triple Integrals to Spherical Coordinates.

X goes from 0 to 2 Y goes from 0 to sqrt(4-x^2) Z goes from 0 to sqrt(4-x^2-y^2).   The function is zsqrt(4-x^2-y^2)dzdydx.   I know the conversion from rectangular... Surface Calculus Multivariable

The two surfaces defined by: xyz=a and (y/x)=b intersect in a space curve. Given a > 0 and b >0, find a general expression for the coordinates of the point on this curve that is closest to the...

Find a linear function whose graph is the plane that intersects the xy-plane along the line y= x+7 and contains the point (-4,-4,-21). Triple Integrals

Describe the region bounded by the planes: x = 0, y=0, z=0, x+y=4, and x=z-y-1.   Describe as a region (in any order you can) the region inside the ball x^2+y^2+z^2=4 and... Lagrange Multipliers

Lagrange multipliers work great for finding the minimum value of y-ax, restricted to the curve y^2-x^2=1 for any a with 0<=a<1 (what is it?) but fails quite miserably if a >=1. Use the geometry... Finding critical points and limits.

Let f(x,y) = 1/(x2 - y) (a) Determine the critical points of f. (b) Does the limit of the function f at the point (0, 0) exist? Justify your answer use cylindrical coordinates to evaluate the triple integral that gives the mass the solid

use cylindrical coordinates to evaluate the triple integral that gives the mass the solid lying under the cone z=10-√(x2+y2), and above the xy-plane, if the density p is given by p(x,y,z)=x2+y2+z2... The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1

The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1 Intersectto form a curvilinear quadrilateral R. The change of variable u=y-x^2, v=y-(x-2)^2 map R onto a square in the uv-plane. Use the... Finding Domain and Range of a Multivariable Function

for the following function find the domain D and range T and show that for every c ∈ T there exists x,y such that f(x,y) = c. Sketch the Domain. The following is my own answer but I am unsure... equation of plane

find equation of a plane that contains the line x=3t y=2+t z=-2t and parallel to the intersection of planes 2x-y=0 and y+z=-1 i dont know what to cross im so confused please help find equation of line through the point (1,-1,1) perpendicular to the line 3x=2y=z and parallel to plane x+y-z=0

i have no idea solving the problem :(( equation of plane that contains point (2,0,3) and line x=-1+t, y=t, z=-4+2t

I tried solving it and I got -x-5y+3z=7 but it seems wrong. Any help please?