Limit calculate using Maclaurin series

Question

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!

Olba12 · Accepted Answer · 2016-05-04 14:48:40Z

0

Hint

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

answered May 4 '16 at 14:48

Olba12

2,31312 silver badges20 bronze badges

$\begingroup$ 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

add a comment |

1 Answer 1