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anonymous

  • 5 years ago

Find the limit: lim (x+1)^x / (x)^x as x->+infinity

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  1. anonymous
    • 5 years ago
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    e

  2. anonymous
    • 5 years ago
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    lim (x+1)^x/x^x= lim [(x+1)/x]^x= lim [x/x + 1/x]^x= lim (1 + 1/x)^x as x-> infinity, 1/x= 0, therefore lim (1 +1/x)^x = (1 + 0) ^infinity= 1^infinity = 1 since 1 power to anything always equals 1

  3. anonymous
    • 5 years ago
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    i think you missed something but according to my calculations the answer is e

  4. anonymous
    • 5 years ago
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    you actually cannot eliminate 1/x as it is not seperate

  5. anonymous
    • 5 years ago
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    the answer to 1.0000001^1000000000000 equals 2.792 , try it

  6. anonymous
    • 5 years ago
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    TI-89 also shown e, but at least you should show him how you solved this

  7. anonymous
    • 5 years ago
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    as lim (x+1)^x / (x)^x as x->+infinity becomes inf/inf form as x goes to inf so we use L hopitles rule but the derivative still does not give us th required results as it too remains inf / inf so we use series expansion which is e+ e/2x +11e/24x^2..... as the terms with x in denominator get 0 as x->inf so we are left with e

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