Establishing the limit of a rational function using epsilon-N

Proving a limit using the epsilon-N definition

[krisretro]

This was a really good explanation. It solidified my understanding of limits of a sequence. Thank you very much

[SumbaSlice]

This is hands down the best explanation I ever saw

[dylanico]

How can we know for sure that 19/9n < e? is it not a case where 19/9n is greater than |an-l|, which means it could be greater than e?

[georgeanton]

Hi! Thank you for the video; question... at around 3:40, we claim $n > 19/9e$. Thus is it necessary to "choose N > 19/9e" or can we just set $N = 19/9e$ since $n > N$ by implication.

[hasnathjahan]

Wow.. I can go to sleep now.. It helped my assignment.

[Maka]

For the final step when you plugged in your N and simplified to epsilon, what do you do if your N doesn't simplify down to just epsilon? I have a constant term in my N that I can't get rid of.

[zhengbozhou]

why you delete the absolute sign directly?

[satibomofficial]

Sir i need help show That the limit of the sequence <Sn> where Sn = 2n/n+4 is 2