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limit does not exist when `a=pi//6``L=-1` when `a=pi``L=1` when `a=pi//2``L=1` when `a=0`

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CSolution :

`underset(xtooo)lim[((e)/(1-e))((1)/(e)-(x)/(1+x))]^(x)=e^(underset(xtooo)lim[((e)/(1-e))((1)/(e)-(x)/(1+x))-1]x)` <br> `=e^(underset(xtooo)lim[(1)/(1-e)-(e)/(1-e)(x)/(1+x)-1]x)` <br> `=e^(underset(xtooo)lim[(e)/(1-e)-(e)/(1-e)(x)/(1+x)]x)` <br> `=e^(underset(xtooo)lim(e)/(1-e)[1-(x)/(1+x)]x)` <br> `=e^((e)/(1-e)underset(xtooo)lim(x)/(1+x))` <br> `=e^((e)/(1-e)underset(xtooo)lim(1)/(1+(1)/(x)))` <br> `=e^((e)/(1-e))`