\(=lim_{x->1}\left(\dfrac{\sqrt[3]{3x-2}-1+x^3+3x^2-4}{x-1}\right)\)
\(A=\sqrt[3]{3x-2}-1+x^3+3x^2-4\)
\(=\dfrac{3x-2-1}{\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{3x-2}+1}+x^3-x^2+4x^2-4\)
\(=\dfrac{3x-3}{\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{\left(3x-2\right)}+1}+x^2\left(x-1\right)+4\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(\dfrac{3}{\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{3x-2}+1}+x^2+4x+4\right)\)
=>\(=lim_{x->1}\left(\dfrac{\sqrt[3]{3x-2}-1+x^3+3x^2-4}{x-1}\right)\)
\(=\lim\limits_{x\rightarrow1}\dfrac{3}{\sqrt[3]{\left(3x-2\right)^2}+\sqrt[3]{3x-2}+1}+x^2+4x+4\)
\(=\dfrac{3}{\sqrt[3]{\left(3\cdot1-2\right)^2}+\sqrt[3]{3\cdot1-2}+1}+1^2+4\cdot1+4\)
\(=\dfrac{3}{1+1+1}+9=1+9=10\)
