Question

does the limit x^2-y^2/x^2 exsist

Answer 1

is it path dependent or not

Answer 2

at what point? x ->0 and y -> 0?

Answer 3

ok trivial but (x,y)-->0

Answer 4

Ok, you should use squeeze theorem,
Define 2 functions, 1 greater, one less and prove they both go to 0 and you can prove the above does too (which it does, you can see this from the graph)

Answer 5

but im wondering if the direction you come from is path dependent, meaning limit doesnt matter what place you come from to (0,0) or it does depend on the path you take

Answer 6

no, not path dependent, it's the limit from everywhere otherwise it would NOT exist

Answer 7

this is where the graph is the most helpful, if you're working on a mac there's a 3d graphing program built in

Answer 8

pc ;( ty for the help

Answer 9

http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/

Answer 10

this is what its supposed to look like
http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/

Answer 11

but its a cool 3d view