Much like the calc 1 limits they are just the value approaching, but now in more variables^TM
Solving limits
1. Algebra
Rational Limits
much like their 2d counterpart we must see if they are defined, and we HAVE to factor sadly LHR doesn’t work here
Rational but with roots
we just take the conjugate :)
Substitution
nonlinear function (xy)
We would take the multipled function to be a variable then we would compute the limit in that single varible (only works for the same destination coord)
We can take each variable to be another like x=y2 to see if we get a number, but we must see that in another path they approach the same limit, if not the limit doesn’t exist
“Separable”
where there are functions but they are ugly (remember)
we would just factor everything so that way each variably is in seprate forms and just being multiplied by each other, so then we “sepratate” it to take the 1d limit of each
Polar Method
we can do this when xy is approaching the origin
Squeeze theorem
Contour and Level curves
The contour curve of height k on the surface z=f(×,y) is the intersection of the surface and the plane z=k, the vertical projection of this contour curve into xy-plane is the level curve f(x,y)=k
its the topographic map guy
Level surface is just the crosssection of the curve
