4.
\((1) \overset{⇀}{a}=\left(x,3\right)\;,\; \overset{⇀}{b}=\left(2\;,\;-1\right) \) ,若\( \overset{⇀}{a} \)与\( \overset{⇀}{b} \)的夹角为锐角,则\(x\)的范围是________________.
\((2)\)数列\(\left\{{a}_{n}\right\} \)的通项公式为\({a}_{n}=2n-1+ \dfrac{1}{{2}^{n}} \),则数列\(\left\{{a}_{n}\right\} \) 的前\(n\)项和为________________.
\((3)\) 若函数\(f\left(x\right)=\cos 2x+a\sin x \)在区间\(\left( \dfrac{π}{6}\;,\; \dfrac{π}{2}\right) \)上是减函数,则\(a\)的取值范围是________________.
\((4)\) 设函数\(y=\begin{cases}-{x}^{3}+{x}^{2}\;,\;x < e \\ a\ln x\;,\;x\geqslant e\end{cases} \)的图象上存在两点 \(P\),\(Q\),使得\(∆POQ \)是以\(O\)为直角顶点的直角三角形\((\)其中\(O\)为坐标原点\()\),且斜边的中点恰好在\(y\)轴上,则实数\(a\)的取值范围是________________.