①当|x|>1时lim(x²ⁿˉ¹+x²)/(x²ⁿ+1)=lim (1+x³ˉ²ⁿ)/(x+x¹ˉ²ⁿ)=1/xn→∞②当|x|<1且x≠0时lim(x²ⁿˉ¹+x²)/(x²ⁿ+1)=x²n→∞③当 x=0时lim(x²ⁿˉ¹+x²)/(x²ⁿ+1)=0n→∞结合①②③，x∈时，极限均存在，f(x)连续
