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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    just to clarify, this is \[\lim_{x \rightarrow \infty}5^{1/x}/(3/x)\]

  2. anonymous
    • 5 years ago
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    if that's correct... then you can imagine you're plugging in "infinity" for where x is

  3. anonymous
    • 5 years ago
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    so 5^(1/INF) becomes 5^0

  4. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    damnit - you were too fast - but yeah - that's correct.

  6. anonymous
    • 5 years ago
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    then the denominator will become a super small number. (approaches 0...)

  7. anonymous
    • 5 years ago
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    and then think about what happens when you have anything over an infinitely small number

  8. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    or if you invert the denominator and multiply, you'll have x on top, which will get really really huge :)

  10. anonymous
    • 5 years ago
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    therefore answer = \[\infty\]

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