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anonymous

  • one year ago

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  1. anonymous
    • one year ago
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    I got infinity but its looking for a number.

  2. anonymous
    • one year ago
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    Just to clarify, you're asking to evaluate\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}\]

  3. anonymous
    • one year ago
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    Yes

  4. anonymous
    • one year ago
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    You're definitely right then...this limit definitely goes to infinity. There are several ways to show this, but easiest way is L'Hopital's Rule.\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}=\lim_{x\rightarrow\infty}\frac{8e^{8x}-8}{2x}=\lim_{x\rightarrow\infty}32e^{8x}=\infty\]

  5. anonymous
    • one year ago
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    So theres no numerical answer you can get for that?

  6. anonymous
    • one year ago
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    Because it says a numerical answer is expected.

  7. anonymous
    • one year ago
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    Nope, this limit doesn't "converge" to any numerical answer. It just grows infinitely. That also makes sense because the function \(e^{8x}\) in the numerator grows WAY faster than \(x^2\) in the denominator, so the limit would never approach a finite number.

  8. anonymous
    • one year ago
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    Alright thank you so much!!

  9. anonymous
    • one year ago
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    No problem. :)

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