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For this question, should I use differentiation method or the integration method ?

$\lim_{x\to \infty} (\frac{x}{x+2})^{x/8}$

this is what i got so far:

Note: $\lim \limits_{n\to\infty} [1 + (a/n)]^n = e^{\underline{a}}\ldots\ldots (1)$

$$ L = \lim \left[\frac{x}{x+2}\right]^{x/8} = \lim\left[\frac{1}{\frac{x+2}{x}}\right]^{x/8} =\frac{1}{\lim [1 + (2/x)]^x]^{1/8}} $$


but i'm not sure where to go from there

  • 0
    In the statement of the Lemma you start with $y_1$, but in the proof you refer to $y_0$.2012-04-06
  • 0
    What happened to your previous question? Do you still need help with it?2012-04-06
  • 0
    In the future, please don't use the edit feature to change a question to a completely different one. Instead, ask a new question. You can then delete the previous question if you want (unless it already has answers).2012-04-06

2 Answers 2