设\(x\)、\(y\)满足\(\begin{cases}\begin{matrix}2x+y\geqslant 4 \\ x-y\geqslant -1\end{matrix} \\ x-2y\leqslant 2\end{cases} \)，若\(z=ax+y\)有最大值无最小值，则\(a\)的取值范围是 \((\)    \()\)．

变量\(x\)，\(y\)满足约束条件\(\begin{cases} & x\geqslant 1 \\ & x-y+1\leqslant 0 \\ & y\geqslant 2(x-1) \end{cases}\)，则目标函数^{\(z={{x}^{2}}+{{y}^{2}}\)}的最小值是\((\)    \()\)

\((1)\)函数\(f(x)={a}^{x-2015}+2017 (a > 0\)且\(a\neq 1)\)所过的定点坐标为__________．

\((2)\)如图，在三棱锥\(P-ABC\)中，\(PA⊥\)平面\(ABC\)，\(AB⊥BC\)，\(PA=AB=1\)，\(BC=\sqrt{3} \)则三棱锥\(P-ABC\)外接球的表面积为__________．

\((3)\)直线\(ax+(a-1)y+1=0\)与直线\(4x+ay-2=0\)互相平行，则实数\(a=\)________．

\((4)\)若变量\(x\)，\(y\)满足约束条件\(\begin{cases}x\leqslant 1 \\ x+y\geqslant 0 \\ 3x-2y+5\geqslant 0\end{cases} \)，\(z=2x-y\)，则\(z\)的最小值为_______．

当\(x\)，\(y\)满足\(\begin{cases}0⩽x⩽2 \\ y⩾0 \\ y⩽x+1\end{cases} \)时，则\(t=x-2y \)的最小值是__________

\(( 1 )\)已知向量\( \overset{→}{a}, \overset{→}{b} \)，满足\( \overset{→}{a}=(1,3) \)，\(\left( \overset{→}{a}+ \overset{→}{b}\right)⊥\left( \overset{→}{a}- \overset{→}{b}\right) \)，则\(\left| \overset{→}{b}\right| =\)______．

\(( 2 )\)已知实数\(x\)，\(y\)满足\(\begin{cases}x\leqslant 3 \\ x+y-3\geqslant 0 \\ x-y+1\geqslant 0\end{cases} \)，则\({x}^{2}+{y}^{2}- \dfrac{1}{2} \)的最小值是     ．

\(( 3 )\)若\(\left(x+3\right)(1- \dfrac{2}{ \sqrt{x}}{)}^{n} \)的展开式中常数项为\(43\)，则\(∫_{2}^{n}2xdx= \)__________．

\(( 4 )\)已知数列\(\left\{{a}_{n}\right\},\left\{{b}_{n}\right\} \)满足\({b}_{n}={\log }_{2}{a}_{n},n∈{N}^{*} \)，其中\(\left\{{b}_{n}\right\} \)是等差数列，且\({a}_{9}{a}_{2009}=4 .\)则\({b}_{1}+{b}_{2}+{b}_{3}+⋯+{b}_{2017}= \)__________．

\((1)\)若\(\sin \alpha =-\dfrac{5}{13}\)，且\(α\)为第四象限角，则\(\tan α\)的值等于________．

\((2)\)已知\(x\)，\(y\)满足约束条件\(\begin{cases} & x-y\leqslant 0, \\ & x+y\geqslant 4, \\ & y\leqslant 4, \\ \end{cases}\)则\(z=2x+3y\)的最大值为________．

\((3)\)已知\(l_{1}\)，\(l_{2}\)分别为双曲线\(\dfrac{{{x}^{2}}}{{{a}^{2}}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > 0,b > 0)\)的两条渐近线，且右焦点关于\(l_{1}\)的对称点在\(l_{2}\)上，则双曲线的离心率为________．

\((4)\)已知函数\(f(x)\)的定义域为\(R\)，直线\(x=1\)和\(x=2\)是曲线\(y=f(x)\)的对称轴，且\(f(0)=1\)，则\(f(4)+f(10)=\)________．