anonymous
  • anonymous
How do you find the limit as x goes to infinity of 5^1/x divide by 3/x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
just to clarify, this is \[\lim_{x \rightarrow \infty}5^{1/x}/(3/x)\]
anonymous
  • anonymous
if that's correct... then you can imagine you're plugging in "infinity" for where x is
anonymous
  • anonymous
so 5^(1/INF) becomes 5^0

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anonymous
  • 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... ?
anonymous
  • anonymous
damnit - you were too fast - but yeah - that's correct.
anonymous
  • anonymous
then the denominator will become a super small number. (approaches 0...)
anonymous
  • anonymous
and then think about what happens when you have anything over an infinitely small number
anonymous
  • 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
anonymous
  • anonymous
or if you invert the denominator and multiply, you'll have x on top, which will get really really huge :)
anonymous
  • anonymous
therefore answer = \[\infty\]

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