(1) numerator denominator divided by x at the same time? y？ The denominator tends to +∞, the numerator is 1, and the limit is 0.

(3) let x? +y？ =u, u->0+ becomes the limit problem of a univariate function, and the u in the numerator and denominator is omitted by Robida's rule or the numerator and denominator are simultaneously × [√ (1+u)+1];

(5) denominator-> 0, molecular constant 1, limit ∞;

(7) Replace with (3), general limit.