如何求斜渐近线?Y=(（2+X）^(3/2）)/X^(1/2)的斜渐近线?

设斜渐近线为y=ax+b
lim(x->+∞) Y/y = 1
= lim(x->+∞) (2+x)^1.5 /( x^0.5 (ax +b)) ,( 上下同时除以x^1.5 )
= lim(x->+∞) (2/x + 1)^1.5 /( a + b/x)) = 1
则a=1
lim(x->+∞) Y-y = 0
= lim(x->+∞) (2+x)^1.5 / x^0.5 -(ax +b) ,( 分式上下同时除以x^1.5 )
= lim(x->+∞) x(2/x+1)^1.5 -(ax +b) ,等价无穷小展开
= lim(x->+∞) x(1+ 1.5*2/x) -(ax +b)
= lim(x->+∞) 1.5*2 - b = 0
b=3