设函数f(X)在x=0点的某邻域内可导,f(0)=0 f'(0)=1/2 ,求lim(x->0)f(2x)/x

问题描述:

设函数f(X)在x=0点的某邻域内可导,f(0)=0 f'(0)=1/2 ,求lim(x->0)f(2x)/x

f(2x)/x = 2 [f(2x) - f(0)] / (2x - 0)
取极限得,lim(x→0) f(2x)/x = 2f'(0) = 1
注意:右边就是f(x)在x=0处的导数