已知f(x)在x=0处可导,且f(0)=0,f'(0)=2,则lim(x→0)[f(sin3x)]/x=____.

问题描述:

已知f(x)在x=0处可导,且f(0)=0,f'(0)=2,则lim(x→0)[f(sin3x)]/x=____.

f(sin3*0)=f(0)=0,x=0
所以f(sin3x)/x是0/0型
使用罗比达法则,得到f'(sin3x)cos3x * 3/ 1=3cos3xf'(sin3x)
代入0得到,3cos0 *f'(sin0)=3*f'(0)=6