求证明极限lim(x,y)->(0,0) (x^2 * sin^2y)⼀x^2 +9y^2 =0

如题,求证明该极限=0
2025-06-22 07:43:03
推荐回答(1个)
回答1:

x^2/(x^2+9y^2)So
所以
0
≤|(x^2 * sin^2y)/(x^2 +9y^2)-0|
=|x^2/(x^2+9y^2)|*sin^2 y
≤1*sin^2 y
=sin^2y
取极限可得sin^2y->0
所以由夹逼法则,

lim(x,y)->(0,0) (x^2 * sin^2y)/(x^2 +9y^2) =0