Is Limsup of Upper Semicontinuous Function True? Help Needed

[ozkan12]

for any upper semicontinuous function limsup f(x)=lim f(x)...Is thıs true ? I don't know, please help me :)

 

[Fallen Angel]

No,

Just think in $f(x)=sin(x)$, is continuous and its upper limit is 1 when $x\to +\infty$