El_Arrow
  • El_Arrow
need help finding the limit
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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El_Arrow
  • El_Arrow
\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n*3^n }\]
freckles
  • freckles
you can say what is happening to the bottom there as n gets big?
Astrophysics
  • Astrophysics
Let it be \[\frac{ \lim_{n \rightarrow \infty} 1 }{ \lim_{n \rightarrow \infty} n3^n}\]

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More answers

El_Arrow
  • El_Arrow
its getting closer to 0?
freckles
  • freckles
are you saying that about the whole fraction?
El_Arrow
  • El_Arrow
no just the bottom
Astrophysics
  • Astrophysics
Noppppe
El_Arrow
  • El_Arrow
the whole fraction?
Astrophysics
  • Astrophysics
I mean if we look at the denominator as freckles is telling you, would you really think it's approaching 0?
El_Arrow
  • El_Arrow
i would think
Astrophysics
  • Astrophysics
You 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
  • freckles
\[5 \cdot 3^5 \text{ big number } \\ 100 \cdot 3^{100} \text{ Even bigger number } \\ 1000 \cdot 3^{1000} \text{ much much more bigger }\]
El_Arrow
  • El_Arrow
yeah its definitely going to infinity
Astrophysics
  • Astrophysics
yeah haha, so what will the whole thing be?
Astrophysics
  • Astrophysics
Note the numerator is 1!!
El_Arrow
  • El_Arrow
1/infinty=0
Astrophysics
  • Astrophysics
Right!
El_Arrow
  • El_Arrow
so you dont do the 1/n/n/n * 3^n/n thing?
El_Arrow
  • El_Arrow
nvm
El_Arrow
  • El_Arrow
thanks both of you
Astrophysics
  • Astrophysics
Np :)
freckles
  • freckles
ditto
Astrophysics
  • Astrophysics
I 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
  • zzr0ck3r
In general we are using \(n\) for sequenes and \(x\) for real numbers, but a sequence is just a function from the naturals.
Astrophysics
  • Astrophysics
Right!
freckles
  • freckles
\[\text{ \let } f: \mathbb{R} \rightarrow \mathbb{R} \text{ be defined by } f(n)=n^2 \] you can use n or any letter there to represent the input.
Astrophysics
  • Astrophysics
Alright, thank you :)
zzr0ck3r
  • zzr0ck3r
Here I assume you have a sequence and you are to have as inputs 1,2,3,4,5....
zzr0ck3r
  • zzr0ck3r
same answer either way...
zzr0ck3r
  • zzr0ck3r
42
Astrophysics
  • Astrophysics
A 9+10 reference and hitchhikers guide in the same post, welp...

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