It is proved that for any point x0∈[a, b], since f(x) is continuous, lim (x->; x0-)f(x)= lim(x-& gt； X0+) f(x)=f(x0) because cosx is continuous. So lim (x->; x0-)cosx = lim(x-& gt； x0+)cosx = cosx 0 so lim(x->； x0-)f(x)cosx =[lim(x-& gt； x0-)f(x)]*[lim(x-& gt； x0-)cosx]= f(x0)cosx 0 lim(x-& gt； x0+)f(x)cosx =[lim(x-& gt； x0+)f(x)]*[lim(x-& gt； x0+)cosx]= f(x0)cosx 0 so lim(x->； x0-)f(x)cosx = lim(x-& gt； x0+) f(x)cosx=f(x0)cosx0