limx→01−cosxx
LHL=limh→0−1−cos(−h)−h
=limh→0−1−cosh−h
=limh→0−1−1+2sin2h2−h
=limh→0−2sin2h2−(h2)2h×(h2)2
=limh→0−−24×h=−12×0=0
RHL=limh→0+1−cos(h)h
=limh→0+1−cosh−h
=limh→0+1−1+2sin2h2h
=limh→0+2sin2h2(h2)2h×(h2)2
=limh→0+24×h=12×0=0
LHL=RHL=0
Hence limx→01−cosxx=0