$\begin{aligned} f(x)= & \frac{1-x(1+|1-x|)}{|1-x|} \cos \left(\frac{1}{1-x}\right) \\ x \rightarrow 1^{+} \quad & \lim _{h \rightarrow 0} \frac{1-(1+h)[1+h]}{(h)} \cos \left(\frac{1}{h}\right) \\ & \Rightarrow \quad \lim _{h \rightarrow 0} \frac{-\left(h^2+2 h\right)}{h} \cos \left(\frac{1}{h}\right) \\ & \Rightarrow \quad(2) \times(-1,1) \text { does not exist }\end{aligned}$ $\begin{aligned} x \rightarrow 1^{-} \quad & \lim _{h \rightarrow 0} \frac{1-(1-h)[1+h]}{(h)} \cos \left(\frac{1}{h}\right) \\ & \lim _{h \rightarrow 0}\left(\frac{1-\left(1-h^2\right)}{(h)}\right) \cos \left(\frac{1}{h}\right) \\ \Rightarrow \quad & 0\end{aligned}$