limx→−πx+πsinx=

RHL=limx→-π+|x+π|sinx=limh→0|-π+h+π|sin(-π+h)=limh→0|h|-sin(π-h)=limh→0h-sinh=-1 LHL=limh→-π-|x+π|sinx=limh→0|-π-h+π|sin(-π-h)=limh→0|-h|-sin(π+h)=limn→0hsinh=1∴L.HL≠RHL⇒ limit does not exist