f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
问题描述：
f(x)=x^2sin(1/x),x不=0.x=0,f(x)=0.求它的渐近线方程
答
设渐近线方程：y=kx+bk=lim【x→∞】f(x)/x=lim【x→∞】xsin(1/x)=lim【x→∞】x·1/x=1b=lim【x→∞】f(x)-kx=lim【x→∞】x^2·sin(1/x)-x=lim【x→∞】x^2·[(1/x)-(1/x)^3/3!+o(1/x^3)]-x=lim【x→...