求解高数极限运算的概念d极限加法的运算 不是必须A和B都存在极限才能拆开吗即极限的和的和的极限上式3XSIN(1/X)

lim(x-> ∞) (3xsin(1/x) + (1/x)sin3x )
=lim(x-> ∞) 3xsin(1/x) + lim(x-> ∞)(1/x)sin3x
lim(x-> ∞) 3xsin(1/x)
=lim(y->0) 3siny/y
= 3
|sin3x| ≤1
lim(x-> ∞)(1/x)sin3x =0
ie
lim(x-> ∞) (3xsin(1/x) + (1/x)sin3x )
=lim(x-> ∞) 3xsin(1/x) + lim(x-> ∞)(1/x)sin3x
= 3+0
=3