The discussion revolves around evaluating a set of mathematical statements related to limits and L'Hospital's rule. Participants are attempting to clarify their understanding of which statements are true or false based on their interpretations of the rules of calculus.
The discussion is ongoing, with participants actively questioning each other's reasoning and interpretations. Some guidance has been offered regarding the conditions necessary for applying L'Hospital's rule, and there is a recognition of potential misunderstandings in the evaluation of specific limits.
Participants are working from a visual reference that is not included in the discussion, which may lead to varying interpretations of the statements being evaluated. There is a noted emphasis on the importance of the behavior of functions as they approach certain limits.
Slimsta said:whats wrong with it? I am 100% sure and i can explain each one!
clamtrox said:Then you just answered your own question. :-)
HallsofIvy said:What exactly is your question? In your first post you said "im 100% sure and i can explain each one!"
The only question I can find is in your second post, "is the 3rd one right? i mean, f/g has to be g cannot = 0.. but its not in the lhospital rule... " In order that we be able to use L'Hospital's rule directly, we must have \lim_{x\to a} g'(x)\ne 0 and that's impossible if g'(x)= 0 in some neighborhood of a. We might be able to extend L'Hopital's rule in the case that f'/g' goes to 0/0 itself by using L'Hopital's rule again, but in order for that to work eventually, there must be some nth derivative of g which has non-zero limit at x= a but again, that's impossible if there is some neighborhood of a in which g' is 0.
jgens said:I would reconsider number 6. Just think about what would happen if \lim_{x \to \infty}f(x) = -\infty.