求左右極限,並判定函數在該點的極限是否存在f(x)=arctan(1/x),x=0

求左右極限,並判定函數在該點的極限是否存在f(x)=arctan(1/x),x=0

x→0+時1/x→+∞所以lim(x→0+)arctan(1/x)→limarctan(+∞)=π/2x→0-時1/x→-∞所以lim(x→0-)arctan(1/x)→limarctan(-∞)=-π/2因為lim(x→0+)arctan(1/x)≠lim(x→0-)arctan(1/x)所以函數在該點的極限不存在…