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Brooke_army

  • one year ago

Evaluate the following limit: lim (1+7/x)^x/12 x→∞

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  1. Brooke_army
    • one year ago
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    I got the number 0.583

  2. Brooke_army
    • one year ago
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    the correct answer is 1.79. I'm not sure where i went wrong

  3. hartnn
    • one year ago
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    how did you get 0.583 ? mind showing your work/steps ?

  4. mathmate
    • one year ago
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    is it \( \large \frac{(1+7/x)^x}{12}\) or \( \large (1+7/x)^{x/12} \)

  5. Brooke_army
    • one year ago
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    y=lim (1+7/x)^x/12 ln(y)=lim x/12 ln(1+7/x) \[\frac{ \ln(1+\frac{ 7 }{x} }{\frac{12 }x }\]

  6. Brooke_army
    • one year ago
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    mathmate it's the second

  7. abb0t
    • one year ago
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    \[\lim_{x \rightarrow ∞} \frac{ (1+7)^x }{ 12 }\]

  8. Brooke_army
    • one year ago
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    then i took d/dx to both the numerator and the denominator

  9. Brooke_army
    • one year ago
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    the problem is \[\lim_{x \rightarrow \infty} (1+\frac{ 7 }{ 12})^\frac{ x }{12 }\]

  10. abb0t
    • one year ago
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    In order to use L'hopitals rule, you must have a fraction with a function on the numerator and denominator

  11. hartnn
    • one year ago
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    do you know a general formula \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=...?\]

  12. hartnn
    • one year ago
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    if you know ^ that, then you can put 7/x = y in your limit question first, to bring in that form.

  13. hartnn
    • one year ago
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    if you use the formula, you get the correct answer in just few steps by adjusting the exponent. \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=e\]

  14. Brooke_army
    • one year ago
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    im trying that right now

  15. hartnn
    • one year ago
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    okay :) take your time...

  16. Brooke_army
    • one year ago
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    thanks i got the right answer

  17. hartnn
    • one year ago
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    good! you're welcome ^_^

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