曲线y=e1x2arctanx2+x+1(x-1)(x+2)的渐近线有（）A．1条B．2条C．3条D．4条

Question

曲线y=e(1)/(x2)arctan(x2+x+1)/((x-1)(x+2))的渐近线有（　　）

A．1条
B．2条
C．3条
D．4条

Answer 1

∵

lim

x→∞

e(1)/(x2)arctan(x2+x+1)/((x-1)(x+2))=1•arctan1=(π)/(4)
∴y=(π)/(4)是其水平渐近线
∵

lim

x→0

e(1)/(x2)arctan(x2+x+1)/((x-1)(x+2))=∞
∴x=0是其铅直渐近线
又

lim

x→∞

(y)/(x)=

lim

x→∞

(e(1)/(x2))/(x)arctan(x2+x+1)/((x-1)(x+2))=0
∴没有斜渐近线．
∴有两条渐近线
故选：B．