1) Let f(x)=1−x(1+∣1−x∣)∣1−x∣cos(11−x) for x≠ 1, then A) limx→1+f(x)=0 B) limx→1+f(x) doesnot exist C) limx→1−f(x)=0 D) limx→1−f(x) doesnot exist Answer: Option B,CExplanation:f(x)=1−x(1+∣1−x∣)∣1−x∣cos(11−x) Now, limx→1−f(x) =limx→1−1−x(1+1−x)∣1−x∣cos(11−x) =limx→1−(1−x)cos(11−x)=0andlimx→1+f(x)=limx→1+ 1−x(1−1+x)x−1cos(11−x) =limx→1+−(x+1)cos(1x+1) where x≠ 1 doesnot exist