anonymous
  • anonymous
??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I got infinity but its looking for a number.
anonymous
  • anonymous
Just to clarify, you're asking to evaluate\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}\]
anonymous
  • anonymous
Yes

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anonymous
  • anonymous
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.\[\lim_{x\rightarrow\infty}\frac{e^{8x}-8x-1}{x^2}=\lim_{x\rightarrow\infty}\frac{8e^{8x}-8}{2x}=\lim_{x\rightarrow\infty}32e^{8x}=\infty\]
anonymous
  • anonymous
So theres no numerical answer you can get for that?
anonymous
  • anonymous
Because it says a numerical answer is expected.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Alright thank you so much!!
anonymous
  • anonymous
No problem. :)

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