Question

need help finding the limit

Answer 1

\[\lim_{n \rightarrow \infty} \frac{ 1 }{ n*3^n }\]

Answer 2

you can say what is happening to the bottom there as n gets big?

Answer 3

Let it be \[\frac{ \lim_{n \rightarrow \infty} 1 }{ \lim_{n \rightarrow \infty} n3^n}\]

Answer 4

its getting closer to 0?

Answer 5

are you saying that about the whole fraction?

Answer 6

no just the bottom

Answer 7

Noppppe

Answer 8

the whole fraction?

Answer 9

I mean if we look at the denominator as freckles is telling you, would you really think it's approaching 0?

Answer 10

i would think

Answer 11

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?

Answer 12

\[5 \cdot 3^5 \text{ big number } \\ 100 \cdot 3^{100} \text{ Even bigger number } \\ 1000 \cdot 3^{1000} \text{ much much more bigger }\]

Answer 13

yeah its definitely going to infinity

Answer 14

yeah haha, so what will the whole thing be?

Answer 15

Note the numerator is 1!!

Answer 16

1/infinty=0

Answer 17

Right!

Answer 18

so you dont do the 1/n/n/n * 3^n/n thing?

Answer 19

nvm

Answer 20

thanks both of you

Answer 21

Np :)

Answer 22

ditto

Answer 23

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...

Answer 24

In general we are using \(n\) for sequenes and \(x\) for real numbers, but a sequence is just a function from the naturals.

Answer 25

Right!

Answer 26

\[\text{ \let } f: \mathbb{R} \rightarrow \mathbb{R} \text{ be defined by } f(n)=n^2 \]
you can use n or any letter there to represent the input.

Answer 27

Alright, thank you :)

Answer 28

Here I assume you have a sequence and you are to have as inputs 1,2,3,4,5....

Answer 29

same answer either way...

Answer 30

42

Answer 31

A 9+10 reference and hitchhikers guide in the same post, welp...