## anonymous 5 years ago How do you find the limit as x goes to infinity of 5^1/x divide by 3/x

1. anonymous

just to clarify, this is $\lim_{x \rightarrow \infty}5^{1/x}/(3/x)$

2. anonymous

if that's correct... then you can imagine you're plugging in "infinity" for where x is

3. anonymous

so 5^(1/INF) becomes 5^0

4. anonymous

I am gonna assume, it's like holy43 postet. You just have to think about what happens to the term 5^(1/x) when you plug in a really, really big number for x... ?

5. anonymous

damnit - you were too fast - but yeah - that's correct.

6. anonymous

then the denominator will become a super small number. (approaches 0...)

7. anonymous

and then think about what happens when you have anything over an infinitely small number

8. anonymous

a way you can test is to try and do (1/0.1) then (1/0.01) then (1/0.001) then even (1/0.000001). and you can look at the behavior of how the number changes each time

9. anonymous

or if you invert the denominator and multiply, you'll have x on top, which will get really really huge :)

10. anonymous

therefore answer = $\infty$