曲线f(x)=x-arctanx的斜渐进线方程是什么

Question

曲线f(x)=x-arctanx的斜渐进线方程是什么

Answer 1

k=lim(x->+∞)f(x)/x
=lim(x->+∞)(x-arctanx)/x
=1
b=lim(x->+∞)[f(x)-kx]
=lim(x->+∞)(x-arctanx-x)
=lim(x->+∞)(-arctanx)
=-π/2
所以
渐近线为y=x-π/2
同理
k=lim(x->-∞)f(x)/x
=lim(x->-∞)(x-arctanx)/x
=1
b=lim(x->-∞)[f(x)-kx]
=lim(x->-∞)(x-arctanx-x)
=lim(x->-∞)(-arctanx)
=π/2
所以
渐近线为y=x+π/2