Limits

Question

What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$

Comments

But I am getting $y = e^a$.

Here is the screenshot of derivation:-

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@ Shubhanshu   you did differentiation wrong brother  on right side 1/(at+1) is right   
differntiation of  $(a+at)^{-1} = -1(a+at)^{-2}(a)$

put t=0 you get -a now :)

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Thanks to all.

Thanks, @sumit goyal 1 for pointing out error.