Does the limit of (2y*x^2)/(4x^2-3y) exist as (x,y) -> (1,1)? If so what is the limit?
The Attempt at a Solution
So at first I thought I could just plug (1,1) into the equation and get two. My study buddy said that you have to make sure it approaches the same thing from every direction else the limit DNE. If it approaches the limit from x=0 then it equals zero, and same with y. but if you take the limit with y=x then it comes out to two.
Are we overthinking this? Can't you just plug it in and ignore the "approaching from x=0" since x can't approach from zero because it goes to 1?