Find the minimum distance from the origin to the surface z2 = (x-1)2+(y-1)2

Find the minimum distance from the origin to the surface z2 = (x-1)2+(y-1)2

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).

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...

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...

Use the divergence theorem to evaluate I=S∫∫(4x+3y2+z)dS, Where s is unit sphere x2+y2+z2=1.

Evaluate ffD(x^2+y^2)dA where D is the region in the first quadrant bounded by y=x, y=3x, and xy=3

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...

Find the maximum value of f(x,y) = x2y7 for x,y ≥ 0 on the unit circle

i have no idea solving the problem :((

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...

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

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

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

This is a hard question whaich found in UKMT question test online

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...

I need some help using vectors to find the area of this parallelogram. I use three points to create two vectors with the same initial points and use a 2x2 determinant to compute the cross...

∫∫ √(4v2 + 4u2 + 1) dvdu, with limits of integration 0≤v≤1 & 0≤u≤2 *Note: the entire expression is supposed to be under the square root symbol I have tried...

Evaluate the following integral using any Vector Calculus method The integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of...

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis...

Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the...