Limit of x*sin(1/x) as x approaches infinity || Two Solutions

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Limit of x*sin(1/x) as x approaches infinity || Two Solutions

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... since we don't know in advance if the limit exists or not, therefore it's more cautious to just start writing the expression without limit notation upfront.
Unless, we know in advance the limit exists, by using Cauchy-Schwarz Theorem for instance.

willyh.r.

I've come across this multiple times.

thedarkslayer

Sir, thank ye fer all these videos. I have a really really important question, and that might conceivably be a good topic of a video: if we wanna learn and go deeper at many academic/intellectual fields, how should we study them? One by one, or all the same time? Let's say, would doing like: reading philosophy at 1/3 of the study time in the day, reading novels at the other 1/3, then doing math at the remaining 1/3 be okay? Or, we better go book by book maybe? Like, after finishing a history book, we proceed to a physics book, then to a math book, then to an economics book etc.... Or should we divide our time by weeks, maybe? Like, philosophy week, math week, sociology week etc?? Or maybe 2-3 months periods? I've been struggling on this issue fer a couple of years now and couldn't figure out a proper solution. Yer opinions on this is so important to me... Much respect and admiration from Turkey...

Dave.Mustaine.Is.Genius

I always liked the second one because, despite needing to know derivatives, it is more "analytical" and algebraic. It is nicer to realize it is one because of the value of cosine than using a "common knowledge" about sen x / x approach when x is really small.

Both are kinda of trick, but the second one goes further on why it is one. The first would be better for a computer, tho.

salsichalivre

I remember using the sandwich theorem to prove this limit equals 1 in my real analysis class.

shaneyaw

0:30 to 0:48 please where I can learn more about this important limits. Thanks.

iñigote

what if the x approaches to negative infinity will the answer still be the same ?? tysm

Muna-dxly

Not fully rigorous. Limit of composite function is a theorem that has some requirements in order to use it. It's like using l'Hospital without checking if it's 0/0 or infinity/infinity.

SimsHacks

Does anyone know any yt channel as this one, but about logic?

David-hngz

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