y=[e^(1/x^2)arctan(x^2+x+1)]/[(x-1)(x+2)] 的渐近线有几条

x->0时,y->-无穷
有一条渐近线 x=0
x->无穷时,
lim y=(1*π/2)/无穷=0
x->负无穷时
lim y=(-π/2)/(-无穷)=0
所以有渐近线 y=0
y'=(-2/x³)e^(1/x²)arctan(x²+x+1)(x-1)^(-1)(x+2)^(-1)
+e^(1/x²)[(2x+1)/((x²+x+1)²+1)](x-1)^(-1)(x+2)^(-1)
-e^(1/x²)arctan(x²+x+1)(x-1)^(-2)(x+2)^(-1)
-e^(1/x²)arctan(x²+x+1)(x-1)^(-1)(x+2)^(-2)
lim x->无穷 y'
=0+0-0-0
=0
lim x->-无穷 y'
=0
所以没有斜向的渐近线
渐近线x轴y轴