The discussion revolves around evaluating the limit of the expression x^3 * e^(-x^2) as x approaches infinity. Participants are exploring the application of L'Hôpital's Rule in this context, particularly in handling the form of the limit that arises from the product of an infinite term and an exponential decay term.
The discussion is ongoing, with participants questioning the assumptions behind evaluating limits at infinity and the proper application of L'Hôpital's Rule. Some guidance has been offered regarding the transformation of the expression, but no consensus or resolution has been reached.
There is a focus on understanding the concept of limits at infinity and the behavior of exponential functions, with some participants expressing uncertainty about the meaning of certain terms in the context of limits.
you have to put expression as the ratio of two functions firstsacwchiri said:Im trying to solve this problem using l'hopital but amm not sure how to do it
lim
X->infinite x^3 * e^(-x^2)
soo this infinite * e^-infinite... but from there I am not sure if you can use it to solve this...
sacwchiri said:yeah i thought about that but amm not sure how much is e^-infinite
That sounds like you are saying "how infinite is it"! What you mean is "what number is e^-infinite". (Strictly speaking that is also meaningless- you cannot evaluate a function of real numbers "at infinity", you can only take limits at infinity.) You know, I hope, that e^x increases without bound (i.e. "goes to infinity") as x goes to infinity. You should also know that "e^(-x2) MEANS 1/e^(x2). If A goes to infinity, what does 1/A go to?sacwchiri said:yeah i thought about that but amm not sure how much is e^-infinite