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I need help to calculate this limit using Maclaurin series: $\lim_{x\to \infty}((x^3-x^2+\frac{2}{x})e^{\frac{1}{x}}-\sqrt{x^3+x^6})$

I don't know from where to start. I think I need to to write Maclaurin series for $e^{\frac{1}{x}}$ and then use the remainder somehow... Thanks!

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Hint

$$ e^{\frac{1}{x}} = 1 + \frac{1}{x} + \frac{1}{2x^2} + \frac{1}{6x^3} + D_1$$

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  • $\begingroup$ What should I do with D1? Can you elaborate more please, thanks! $\endgroup$ – Tim May 5 '16 at 9:17
  • $\begingroup$ Did you solve it? $\endgroup$ – Olba12 May 9 '16 at 18:58
  • $\begingroup$ Yes. thanks!!!! $\endgroup$ – Tim May 10 '16 at 18:24

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