Firstly: taking into account that and , by a well-known theorem . Then, you can use an "indecent trick": transport the arguments of that theorem to your problem.
how can I evaluate this limit, using the epsilon delta way if possible. I read my textbook about the method but didn't really understand.
(x,y) -> (0,0) of [x-xy+3]/[x^2y+5xy-y^3]
plugging in the point you can see its discontinuous.
so if I move along the x axis in the end I will get x-3/0 and along the y axis I will get -3/y^3, in the end both of those will be -3/0. If I move along the line y = x I also get the same answer. So I can say the limit does nit exist? Now how can I show this using the epsilon delta method for limits?
hi. Thanks for the reply but I'm not sure if i still understand fully. This theorem, is it the limit of a rational function is the limit of the numerator over the denominator? I am also unsure about this trick I can use to apply the epsilon delta method to my problem.
More correctly, the limit is infinity (or simply does not exist).However your explanation helped! So I can conclude that the limit goes to infinity.