The discussion revolves around the limit of the function e^(1/x) as x approaches 0, with particular attention to the direction from which x approaches 0. Participants are exploring the implications of approaching from the left versus the right.
Some participants have identified potential mistakes in the reasoning presented, particularly regarding the behavior of the function as b approaches 0 from below. There is an acknowledgment of the different outcomes based on the direction of approach, with some guidance offered about the behavior of related terms.
There is a mention of specific terms and limits that may be causing confusion, such as the behavior of x e^(-x) as x tends to +infinity, which is relevant to the limit being discussed.
b approaches 0 from below, so 1/b tends to minus infinity. There is a small mistake: the 1 in the (1 . 0 - 0) term. Need to use the fact that x e-x tends to 0 as x tends to +infinity.Phys12 said:
In this solution, in the last 3rd line, I get the first part (-e^-1 - e^-1), however, after the '-' symbol, the person writes (1/b * e^1/b - e^1/b) and takes the limit as b->0. However, shouldn't this give him (inf. * e^inf - e^inf)?
Thanks
(His answer is correct, by the way)
Ohk! I didn't notice the fact that we were approaching 0 from the left hand side. Thanks! :)haruspex said:
Phys12 said: