lim(sin√(x+1)-sin√x)x→+∞

lim(sin√(x+1)-sin√x)x→+∞

lim(sin√(x+1)-sin√x)x→+∞=lim(sin√(x+1))-lim(sin√x)x→+∞=
lim(sin√x)-lim(sin√x)x→+∞=0