## El_Arrow one year ago need help finding the limit

1. El_Arrow

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

2. freckles

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

3. Astrophysics

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

4. El_Arrow

its getting closer to 0?

5. freckles

are you saying that about the whole fraction?

6. El_Arrow

no just the bottom

7. Astrophysics

Noppppe

8. El_Arrow

the whole fraction?

9. Astrophysics

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

10. El_Arrow

i would think

11. 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?

12. freckles

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

13. El_Arrow

yeah its definitely going to infinity

14. Astrophysics

yeah haha, so what will the whole thing be?

15. Astrophysics

Note the numerator is 1!!

16. El_Arrow

1/infinty=0

17. Astrophysics

Right!

18. El_Arrow

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

19. El_Arrow

nvm

20. El_Arrow

thanks both of you

21. Astrophysics

Np :)

22. freckles

ditto

23. 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...

24. zzr0ck3r

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

25. Astrophysics

Right!

26. 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.

27. Astrophysics

Alright, thank you :)

28. zzr0ck3r

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

29. zzr0ck3r

30. zzr0ck3r

42

31. Astrophysics

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