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Pawanyadav

  • one year ago

Lim{(x+x^-1)e^(1÷x)-x=? Where x tending to infinity.

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  1. geerky42
    • one year ago
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    \[\lim_{x\to\infty} (x+x^{-1})e^{1/x}-x\]?

  2. Pawanyadav
    • one year ago
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    Ya this is the question. what's the solution?

  3. welshfella
    • one year ago
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    Hint : as x approaches infinity 1/x approaches zero so e^1/x will approach 1.

  4. geerky42
    • one year ago
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    \[\lim_{x\to\infty} (x+x^{-1})e^{1/x}-x \\~\\= \lim_{x\to\infty} xe^{1/x}+x^{-1}e^{1/x}-x\\~\\ = \lim_{x\to\infty} x(e^{1/x}-1)+x^{-1}e^{1/x}\] Here, \(x^{-1}e^{1/x}\) approaches to 0. So we are left with \[\lim_{x\to\infty} x(e^{1/x}-1)\\~\\=\lim_{x\to\infty} \dfrac{e^{1/x}-1}{\dfrac{1}{x}}\]From here, use L'Hopital's Rule.

  5. geerky42
    • one year ago
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    @Pawanyadav Does that help?

  6. anonymous
    • one year ago
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    I don't think so because it's not the solution :P

  7. Pawanyadav
    • one year ago
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    Yes absolutly

  8. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  9. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  10. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  11. geerky42
    • one year ago
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    Correct.

  12. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  13. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  14. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  15. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  16. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  17. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  18. geerky42
    • one year ago
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    |dw:1433801268065:dw|

  19. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  20. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  21. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  22. Pawanyadav
    • one year ago
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    The answer After solving is 1.

  23. geerky42
    • one year ago
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    @Zarkon I think something is buggy.

  24. geerky42
    • one year ago
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    I see so many replies "The answer After solving is 1."

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