Question

The tangent plane at (1,1,1) on the surface x2+y2+z2+xy+xz=5 is given by

x+ y+ z=

(all values should be positive whole numbers with no common factors)

Answer #1

Find the equation for the tangent plane to the surface
z=(xy)/(y+x) at the point P(1,1,1/2).

Calculate ∫ ∫S f(x,y,z)dS for the given surface and function.
x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.

5.) a.) Integrate G(x,y,z)=xz over the sphere
x2+y2+z2=9
b.) Integrate
G(x,y,z)=x+y+z over the portion of the plane
2x+y+z=6 that lies in the first octant.

1. a) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the tangent plane at (1, 1, 1).
b) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the normal line to the surface at (1, 1, 1).

Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2,
and E[X2]=E[Y2]=E[Z2]=5.
Find cov(XY,XZ).
(Enter a numerical answer.)
cov(XY,XZ)=
Let X be a standard normal random variable. Another random
variable is determined as follows. We flip a fair coin (independent
from X). In case of Heads, we let Y=X. In case of Tails, we let
Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not...

you are given two vectors:
v=[x2 +y2+ z2, 2xyz,
x+y+2z]
u=[xy+z , xy2 z2 , x+3z]
Calculate the following expressions:
a) curl v
b) grad vz

Determine an equation of the plane tangent to the surface
x2 - 3x + y2 - y + z2 + 2 = 0 at
the point (2, 1, 0).

Given the function f(x, y, z) = (x2 + y2 +
z2 )−1/2
a) what is the gradient at the point (12,0,16)?
b) what is the directional derivative of f in the direction of
the vector u = (1,1,1) at the point (12,0,16)?

Given x2/16 + z2/36 - y2/100 =1
find:
a. The xy, xz, and yz traces
b.Where it intercepts the coordinate axe

Evaluate ∫∫Sf(x,y,z)dS , where f(x,y,z)=0.4sqrt(x2+y2+z2)) and S
is the hemisphere x2+y2+z2=36,z≥0

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