4.求下列极限:-|||-(1) lim _(xarrow infty )(e)^dfrac (1{x)} :-|||-x→∞-|||-(3) lim _(xarrow infty )((1+dfrac {1)(x))}^dfrac (x{2)} ;-|||-(5) lim _(xarrow infty )((dfrac {3+x)(6+x))}^dfrac (x-1{2)} :-|||-(7) lim _(xarrow e)dfrac (ln x-1)(x-e)-|||-(2) lim _(xarrow 0)ln dfrac (sin x)(x) =-|||-(4) lim _(xarrow 0)((1+3{tan )^2x)}^(cos ^2x) ;-|||-(6) lim _(xarrow 0)dfrac (sqrt {1+tan x)-sqrt (1+sin x)}(xsqrt {1+{sin )^2x}-x} =-|||-(8) lim _(xarrow 0)dfrac ({e)^3x-(e)^2x-(e)^x+1}(sqrt [3]{(1-x)(1+x))-1}