1.求下列极限:-|||-(1) lim _(xarrow 0)dfrac ({e)^x-(e)^-x}({e)^x-cos x}-|||-(2) lim _(xarrow pi )dfrac (tan x-1)(sin 4x)-|||-(3) lim _(xarrow 0)dfrac ({e)^x-cos x-x}({x)^2}-|||-(4) lim _(xarrow 1)dfrac (sin (pi sqrt {x))}(ln (3x-2));-|||-(5) lim _(xarrow 2)dfrac ({x)^2-(2)^x}({x)^x-4};-|||-(6) lim _(xarrow 0)dfrac ({e)^2x-(e)^-x-3x}(2sin {x)^2};-|||-(7) lim _(xarrow 0)dfrac (tan x-x)(x-sin x);-|||-(8) lim _(xarrow pi )dfrac (ln sin x)({(pi -2x))^2};-|||-(9) lim _(xarrow +infty )dfrac (xln x)({x)^2+ln x};-|||-(10) lim _(xarrow +infty )dfrac (ln (1+{e)^x)}(sqrt {1+{x)^2}};-|||-(11) lim _(xarrow infty )dfrac (tan x)({tan )^3x};-|||-(12) lim _(xarrow {0)^+}dfrac (ln 3sin 3x)(ln sin x);-|||-(13) lim _(arrow infty )dfrac (ln (x-pi ))(tan x)-|||-(14) lim _(xarrow 0)dfrac (x-arctan x)({tan )^3x};-|||-(15) lim _(xarrow 0)dfrac ((tan x-x)(1-sqrt {1-x))}({x)^2tan xcdot ln (1+x)}-|||-(16) lim _(xarrow 0)dfrac ({e)^x-(e)^-x-2x}(x-sin x)-|||-(17) lim _(xarrow 0)dfrac ({({e)^x-x-1)}^2}(x{sin )^3x}-|||-(18) lim _(xarrow 2)dfrac (cos xcdot ln (x-2))(ln ({e)^x-(e)^2)}-|||-(19) lim _(xarrow 0)dfrac (sin x-xcos x)((1+cos x)ln (1+{x)^3)}-|||-(20) lim _(xarrow 0)dfrac ({tan )^2x-(x)^2}({x)^2tan (x)^2}-|||-(21) lim _(xarrow +infty )dfrac (({x)^2+x)sin x}({e)^x+(x)^2+1}