The discussion revolves around computing the limit of the expression (1 - e^(3x)) / sin(x) as x approaches 0, specifically using L'Hospital's Rule. Participants explore the nature of the limit, the appropriate indeterminate form, and alternative methods such as Taylor expansion.
Participants express differing views on the appropriateness of using L'Hospital's Rule versus Taylor expansion, indicating a lack of consensus on the best approach. There is also some uncertainty regarding the classification of the indeterminate form.
Participants reference the concepts of poles and indeterminate forms, but there is no resolution on the implications of these terms in this context.
Marco_84 said:It is common to taylor expand those kind of functions that become small so you can get something like this:
(1-exp(3x))/sinx =(1-1-3x)/x +0(x^2)=-3.
I don't think you can use de L'Hopital here because you have a pole.
Ben Niehoff said:This is incorrect and confusing.
Taylor expansion and l'Hopital's rule are actually equivalent. And f/g does not have a pole at zero, because the limit is finite. 1/g has a pole, and that is precisely why you use l'Hopital's in the first place.
retrofit81 said:Looks like you applied l'hospital's rule right to me - :)
When you say you're not sure what "type" it is, I'm assuming you mean what kind of indeterminate form? If you look at the function in your limit, actually evaluated at the limit value (x = 0), what kind of form is it? Surely not infinity over infinity... :)