Question

(x²+1)arctanx/x的斜渐近线为

Answer 1

• k=lim(x→+∞)(x²+1)arctanx/x²=π/2

  b=lim(x→+∞)[(x²+1)arctanx/x-½π·x]

  =lim(x→+∞)[(x²+1)arctanx-½π·x²]/x

  =lim(t→0)[(1+t²)arctan(1/t)-½π·]/t

  =lim(t→0)[2t·arctan(1/t)+(1+t²)·/(1+1/t²)·(-1/t²)]/1  0/0型 洛必达

  =lim(t→0)[2t·arctan(1/t)-(1+t²)·/(1+t²)]/1

  =-1

  斜渐近线y=½π·x-1

  同理x→-∞时 斜渐近线y=-½π·x-1

  

Answer 2

简单计算一下即可，答案如图所示

Answer 3