4roommates share the cost of $108 of the electric bill evenly. what is the fraction to represent the division and classify each result by indicating the set or sets to which it belongs.

The answer to this question can be given as:

Tangent line at r(0)[more generally r(to)]  is on tangent plane of S at that point.

Step-by-step explanation:

In option (A):

put x=2 ,y=-2 in Z=x sin(x+y).

Z=2 sin(2+(-2))

Z=2 sin(2-2)

Z=2 sin(0)  

we know that sin o= 0;

so (2,-2,0) ∈ s

dz/dx=sin(x+y)+xcos(x+y)

dz/dx=x cos(x+y)

tangent plane T at (a,-2,0) is:

z-0= dz/dx(2,-2)(x-2)+dz/dy(2,-2)(y+2)

z=(0+2)(x-2)+(2)(y+2)

z=2(x-2)+2(y+2)

z=2x-4+2y+4

z=2x+2y is the plane at(2,-2,0)

In option (B):

r(t) is on s

r'(t) =(a'(t),b'(t),c'(t))

this is  tangent rector on S for Vt

so  r'(0) is  tangent to 5

r'(0) is  parallel to T[tangent plane or 5]

In option (C):

yes.

fact , for any surface S. Choose any curve acts in S

if r'(0)!= 0 or[more generally r'(b)!=0]

=Tangent line at r(0)[more generally r(to)]

is on tangent plane of S at that point.