Hello, I need help with part a. I don't know the exact criteria that makes a function count as a plane, so I'd appreciate it if someone could tell me the definition. More specifically, can planes have x^2 and y^2 values as inputs?
#Definition of a tangent plane
ocean idol
viscid sage
planes must be linear, so no they can't have x² and y² values in the fully simplified equation
and to quote the definition:
"A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors"
z=25+8(x-4)+6(y-3)
because:
f(x,y)+∆x•f_x+∆y•f_y=z but you can probably already do that part
@ocean idol
ocean idol
planes must be linear, so no they can't have x² and y² values in the fully simpl...
this is perfect, thank you so much!
grim geyserBOT
@ocean idol has given 1 rep to @viscid sage
viscid sage
no problem!
@ocean idol cartesian plane equation is this btw:
ax+by+cz=k where k is the distance from (0,0,0) along the axes
which is derived from n•r=k where n is the normal vector to the plane
which can be derived from (bi+cj+dk)+λ(ei+fj+gk)+μ(hi,ij,jk)
where (b,c,d) is a position vector on the plane, (e,f,g) is a linearly independent direction vector to (h,i,j) and so on lmao
it's helpful to have long strings of derivations