If and are sequences converging to the same point such that , and if is differentiable funtion whose derivative is continuous at and which satisfies the condition that , show that .
If and are sequences converging to the same point such that , and if is differentiable funtion whose derivative is continuous at and which satisfies the condition that , show that .
Does actually mean ? If so, I would advise you to use the mean value theorem that guarantees the existence of a such that and
Hence and by continuity of at you conclude...
Last edited by Failure; August 7th 2009 at 08:56 AM.
Aw, I didn't say that. But what I can say is that (why? - because the sequence is sandwiched between two sequences that both converge to ). And thus, we have, by continuity of at :