Let p=limx→0 ln(cos2x)3x2,q=limx→0 sin22xx1-ex and r=limx→1 x−xln⁡x Then p, e, r satisfy

Clearly,p=limx→0 ln⁡(1+cos⁡2x−1)3x2=limx→0 ln⁡(1+cos⁡2x−1)(cos⁡2x−1)⋅cos⁡2x−13x2=−23q=limx→0 sin2⁡2x4x2⋅4x2x1−ex=−4and  r=limx→1 x−xln⁡(1+x−1)=limx→1 x(1−x)ln⁡1+x−1x−1⋅(x−1)=limx→1 x(1−x)ln⁡1+(x−1)x−1⋅(x−1)(1+x)=−12Hence, q < p < r