calc

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Use L’Hopital’s rule to find the limit of this sequence

(n^100)/(e^n)

...If you do L'Hop. Rule it would take forever, right? You would always get an (e^n) at the bottom and will have to use the L'Hop. rule 100 times to find the limit...100*n^99, 9900n^98, and etc.

Is there a shortcut to find the limit?
Or, am I doing something way wrong?

  • calc -

    You didn't say what the aprroach value is for n
    is n---> 0 ?

    lim n^100/e^n)
    = lim (100n^99)/(e^n)
    = lim (9900n^98) / e^n
    = ...
    = lim (huge n^1)/e^n
    = lim (more huge )/e^n
    = lim (0/e^n)
    = 0/1
    = 0

  • calc -

    what if n approaches infinity?

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