已知\(a\in R\)，若\(\dfrac{a+2i}{4-i}\)是纯虚数，则在复平面内，复数\(z=ai+{{i}^{2018}}\)所对应的点位于\((\)    \()\)

\((1)\)计算\({{\log }_{2.5}}6.25+\lg \dfrac{1}{100}+\ln \sqrt{e}+{{2}^{1+{{\log }_{2}}3}} =\)______．

\((2){{\left( \sqrt{x}-\dfrac{i}{x} \right)}^{8}}\)的二项展开式中，含\(x\)的一次项的系数为         \(.(\)用数字作答\()\)

\((3)\)两圆\({{x}^{2}}+{{y}^{2}}+2ax+{{a}^{2}}-4=0\)和\({{x}^{2}}+{{y}^{2}}-4by-1+4{{b}^{2}}=0\)恰有三条公切线，若\(a\in R\)，\(b\in R\)且\(ab\ne 0\)，则\(\dfrac{1}{{{a}^{2}}}+\dfrac{1}{{{b}^{2}}}\)的最小值为_____________．

\((4)\)对于函数\(f\left( x \right)\)，如果\(f\left( x \right)\)可导，且\(f\left( x \right)={f}{{'}}\left( x \right)\)有实数根\(x\)，则称\(x\)是函数\(f\left( x \right)\)的驻点\(.\)若函数\(g\left( x \right)={{x}^{2}}\left( x > 0 \right),h\left( x \right)=\ln x,\varphi \left( x \right)=\sin x\left( 0 < x < \pi \right)\)的驻点分别是\({{x}_{1}},{{x}_{2}},{{x}_{3}}\)，则的大小关系是______\((\)用“\( < \)”连接\().\)   

\((1)\)计算\({\log }_{2.5}6.25+\lg ⁡ \dfrac{1}{100}+\ln ⁡ \sqrt{e}+{2}^{1+{\log }_{2}3} =\)______．

\((2){{\left( \sqrt{x}-\dfrac{i}{x} \right)}^{8}}\)的二项展开式中，含\(x\)的一次项的系数为         \(.(\)用数字作答\()\)

\((3)\)两圆\({{x}^{2}}+{{y}^{2}}+2ax+{{a}^{2}}-4=0\)和\({{x}^{2}}+{{y}^{2}}-4by-1+4{{b}^{2}}=0\)恰有三条公切线，若\(a\in R\)，\(b\in R\)且\(ab\ne 0\)，则\(\dfrac{1}{{{a}^{2}}}+\dfrac{1}{{{b}^{2}}}\)的最小值为_____________．

\((4)\)若函数\(f\left( x \right)\)满足\(f\left( x-1 \right)=\dfrac{1}{f\left( x \right)-1}\)，当\(x\in \left[ -1,0 \right]\)时，\(f\left( x \right)=x\)，若在区间\(\left[ -1,1 \right]\)上，\(g\left( x \right)=f\left( x \right)-mx+m\)有两个零点，则实数\(m\)的取值范围为           ．