Let f be a continuous function on R such that f12n=sinene-n2+2n2n2+1 then the value of f(0) is

for any sequence xn  f(0)=Ltx→0  f(x)=Ltn→∞  f(xn) Such that Ltn→∞xn=0Then f(0)=Ltn→∞  f12n=Ltn→∞sinene−n2+2n2n2+1                                        =Ltn→∞sinene−n2+21+1n2=0+2=2