Ta có $A=\dfrac{(x^{2013}-1)-2(x-1)}{(x^{2014}-1)-2(x-1)}=\dfrac{(x-1)\bigg[x^{2012} +x^{2011}+...+1-2\bigg]}{(x-1)\bigg[x^{2013} +x^{2012}+...+1-2 \bigg]}$Vậy $\lim \limits_{x\to1}A=\lim \limits_{x\to1} \dfrac{x^{2012} +x^{2011}+...+1-2}{x^{2013} +x^{2012}+...+1-2}=\dfrac{2012-2}{2013-2}=\dfrac{2011}{2012}$
Ta có $A=\dfrac{(x^{2013}-1)-2(x-1)}{(x^{2014}-1)-2(x-1)}=\dfrac{(x-1)\bigg[x^{2012} +x^{2011}+...+1-2\bigg]}{(x-1)\bigg[x^{2013} +x^{2012}+...+1-2 \bigg]}$Vậy $\lim \limits_{x\to1}A=\lim \limits_{x\to1} \dfrac{x^{2012} +x^{2011}+...+1-2}{x^{2013} +x^{2012}+...+1-2}=\dfrac{2012-2}{2013-2}=\dfrac{2010}{2011}$
Ta có $A=\dfrac{(x^{2013}-1)-2(x-1)}{(x^{2014}-1)-2(x-1)}=\dfrac{(x-1)\bigg[x^{2012} +x^{2011}+...+1-2\bigg]}{(x-1)\bigg[x^{2013} +x^{2012}+...+1-2 \bigg]}$Vậy $\lim \limits_{x\to1}A=\lim \limits_{x\to1} \dfrac{x^{2012} +x^{2011}+...+1-2}{x^{2013} +x^{2012}+...+1-2}=\dfrac{2012-2}{2013-2}=\dfrac{201
1}{201
2}$