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El_Arrow
 one year ago
need help finding the limit
El_Arrow
 one year ago
need help finding the limit

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El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n*3^n }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.5you can say what is happening to the bottom there as n gets big?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Let it be \[\frac{ \lim_{n \rightarrow \infty} 1 }{ \lim_{n \rightarrow \infty} n3^n}\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0its getting closer to 0?

freckles
 one year ago
Best ResponseYou've already chosen the best response.5are you saying that about the whole fraction?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I mean if we look at the denominator as freckles is telling you, would you really think it's approaching 0?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2You can split it even further as follow \[\lim_{n \rightarrow \infty} n \lim_{n \rightarrow \infty} 3^n\] still think it's approaching 0?

freckles
 one year ago
Best ResponseYou've already chosen the best response.5\[5 \cdot 3^5 \text{ big number } \\ 100 \cdot 3^{100} \text{ Even bigger number } \\ 1000 \cdot 3^{1000} \text{ much much more bigger }\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0yeah its definitely going to infinity

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2yeah haha, so what will the whole thing be?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Note the numerator is 1!!

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so you dont do the 1/n/n/n * 3^n/n thing?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2I have a quick question though, when we do limits, shouldn't we let n = x, otherwise it's not a function, I remember something like that...

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0In general we are using \(n\) for sequenes and \(x\) for real numbers, but a sequence is just a function from the naturals.

freckles
 one year ago
Best ResponseYou've already chosen the best response.5\[\text{ \let } f: \mathbb{R} \rightarrow \mathbb{R} \text{ be defined by } f(n)=n^2 \] you can use n or any letter there to represent the input.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2Alright, thank you :)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0Here I assume you have a sequence and you are to have as inputs 1,2,3,4,5....

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0same answer either way...

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.2A 9+10 reference and hitchhikers guide in the same post, welp...
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