Question

请教函数与方程的题请看图：关键是1/(1+f'(s)f(s)/s)=1/(1+f'(0)^2)这一步什么

Answer 1

Q是P到y=f(x)最近的点则满足PQ⊥Q处的切线

即f'(s)*(f(s)-0)/(s-t)=-1

则t=s+f'(s)f(s)

s/t当t->0的极限相当于

lim(s->0)1/(1+f'(s)f(s)/s)=1/(1+f'(0)^2)=1/(1+a^2)

因为s->0时f'(s)->f'(0),f(s)/s=(f(s)-f(0))/(s-0)->f'(0)