4．
\((1)\)设\(f(x)=\dfrac{1}{x}\)，则\(\underset{x\to 1}{{\lim }}\,\dfrac{f(x)-f(1)}{1-x}=\)
\((2)\)已知函数\(f(x)={{x}^{3}}+a{{x}^{2}}+bx-{{a}^{2}}-7a(a > -5)\)在\(x=1\)处取得极大值\(10\)，则\(\dfrac{a}{b}=\)
\((3)\)已知双曲线\(\dfrac{{{x}^{2}}}{{{a}^{2}}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > 0,b > 0)\)的两条渐近线与圆\({{(x-\sqrt{3})}^{2}}+{{y}^{2}}=1\)均相切，则此双曲线的离心率为____．
\((4)\)已知数列\(\left\{ {{a}_{n}} \right\}\)满足\({{a}_{n+1}}+{{a}_{n}}=(n+1)\cdot \cos \dfrac{n\pi }{2}(n\geqslant 2,n\in {{N}^{*}})\)，\({{S}_{n}}\)是数列\(\left\{ {{a}_{n}} \right\}\)的前\(n\)项和，若\({{S}_{2017}}+m=1010\)，且\({{a}_{1}}\cdot m > 0\)，则\(\dfrac{1}{{{a}_{1}}}+\dfrac{1}{m}\)的最小值为