Question

x=a(cost+tsint)的导数为?

Answer 1

dx/dt=-asint+asint+atcost=atcost d^2x/dt^2=acost-atsint dy/dt=acost-acost+atsint=atsint d^2y/dt^2=asint+atcost 所以d^2y/dx^2=(d^2y/dt^2)/(d^2x/dt^2) =(asint+atcost)/(acost-atsint) 设渐进线是y=ax+b a=lim 根号下(x^2-1)/x=1，x趋于无穷大 b=lim (y-x),x趋于1时 =lim 根号下(x^2-1)-x=-1 所以渐进线是y=x-1