2.
\((1)\)计算定积分\(∫_{−1}^{2} \sqrt{4−{x}^{2}}dx= \)________.
\((2)\)设变量\(x\),\(y\)满足不等式组\(\begin{cases} & x+y-4\leqslant 0 \\ & x-3y+3\leqslant 0 \\ & x\geqslant 1 \end{cases}\),则\(z=\dfrac{|x-y-4|}{\sqrt{2}}\)的取值范围是________.
\((3)\)已知椭圆\(\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)\)的左、右焦点分别为\(F_{1}(-c,0)\),\(F_{2}(c,0)\),若椭圆上存在点\(P\)使\(\dfrac{a}{\sin \angle P{{F}_{1}}{{F}_{2}}}=\dfrac{c}{\sin \angle P{{F}_{2}}{{F}_{1}}}\)成立,则该椭圆的离心率的取值范围为________.
\((4)\)用\(g(n)\)表示自然数\(n\)的所有因数中最大的那个奇数,例如:\(9\)的因数有\(1\),\(3\),\(9\),\(g(9)=9\),\(10\)的因数有\(1\),\(2\),\(5\),\(10\),\(g(10)=5\),那么\(g(1)+g(2)+g(3)+…+g(2^{2015}-1)=\)________.