1.简答题-|||-.lim _(xarrow 1)dfrac ({x)^2-2x+1}({x)^2-1}-|||-

本题考查的是极限的计算，分式的变形，分式的化简。$\lim _{x\rightarrow \infty }(\dfrac {{x}^{3}}{2{x}^{2}-1}-\dfrac {{x}^{2}}{2x+1})$$=\lim _{x\rightarrow \infty }(\dfrac {{x}^{3}+{x}^{2}}{2{x}^{2}-1}-\dfrac {{x}^{3}+{x}^{2}}{2x+1})$$=\lim _{x\rightarrow \infty }(\dfrac {{x}^{3}+{x}^{2}}{{x}^{3}+{x}^{2}}-\dfrac {{x}^{2}-1}{2x+1})\cdot \dfrac {1}{{x}^{3}+{x}^{2}}$$=\lim _{x\rightarrow \infty }(\dfrac {1}{{x}^{3}+{x}^{2}}-\dfrac {1}{2x+1})\cdot \dfrac {1}{{x}^{3}+{x}^{2}}$$=\lim _{x\rightarrow \infty }(\dfrac {1}{{x}^{3}+{x}^{2}}-\dfrac {1}{2x+1})\cdot \lim _{x\rightarrow \infty }\dfrac {1}{{x}^{3}+{x}^{2}}$$=\dfrac {1}{2}$