Question

一道高数题追加50分求解

请问蓝色波浪线地方怎么得来的呢

Answer 1

简单计算一下即可，答案如图所示

Answer 2

f(x)
=x^3.sin(1/x)；x≠0
=0；x=0
lim(x->0)x^3.sin(1/x)=0=f(0)
x=0，f(x)连续
f'(0)
=lim(h->0)[h^3.sin(1/h)-f(0)]/h
=lim(h->0)h^2.sin(1/h)
=0
x≠0
f'(x)
=3x^2.sin(1/x)+x^3.cos(1/x).(-1/x^2)
=3x^2.sin(1/x)-x.cos(1/x)
f''(0)
=lim(h->0)[3h^2.sin(1/h)-h.cos(1/h)-f'(0)]/h
=lim(h->0)[3h.sin(1/h)-cos(1/h)]
不存在
x=0，不是极值点

Answer 3

简单的乘数
[1 + (dy/dx)^2 ] dy/dx
=dy/dx + (dy/dx).(dy/dx)^2
=dy/dx + (dy/dx)^3