Let $f\left(x\right)=\frac{1-x\left(1+\left|1-x\right|\right)}{\left|1-x\right|}\cos \left(\frac{1}{1-x}\right)$ for $x\ne 1.$ Then: (A)${\left(\lim \right)}_{n\to 1^{-}}f\left(x\right)$ does not exist (B)${\left(\lim \right)}_{n\to 1^{+}}f\left(x\right)$ does not exist (C)${\left(\lim \right)}_{n\to 1^{-}}f\left(x\right)=0$ (D)${\left(\lim \right)}_{n\to 1^{+}}f\left(x\right)=0$

Views: 1,266 students