\(=\lim\limits_{x\rightarrow2}\dfrac{\sqrt{x-1}-1+x^4-3x^3+x^2+4}{\sqrt{2x}-2}=\lim\limits_{x\rightarrow2}\dfrac{\dfrac{x-2}{\sqrt{x-1}+1}+\left(x-2\right)^2\left(x^2+x+1\right)}{\dfrac{2\left(x-2\right)}{\sqrt{2x}+2}}\)
\(=\lim\limits_{x\rightarrow2}\dfrac{\dfrac{1}{\sqrt{x-1}+1}+\left(x-2\right)\left(x^2+x+1\right)}{\dfrac{2}{\sqrt{2x}+2}}=1\)