37:
\(\lim\limits_{x\rightarrow1}\dfrac{x^4-x^3-x+1}{x^3-5x^2+7x-3}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{x^3\left(x-1\right)-\left(x-1\right)}{x^3-x^2-4x^2+4x+3x-3}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{\left(x-1\right)\left(x^3-1\right)}{\left(x-1\right)\left(x^2-4x+3\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{\left(x-1\right)\cdot\left(x^2+x+1\right)}{\left(x-1\right)\left(x-3\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{x^2+x+1}{x-3}=\dfrac{1+1+1}{1-3}=\dfrac{3}{-2}=-\dfrac{3}{2}\)
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