F(x)=f(x)(1+|sinx|),F(x),f(x)在x=0处可导,求f(0)
问题描述:
F(x)=f(x)(1+|sinx|),F(x),f(x)在x=0处可导,求f(0)
答
F'(0)=lim{x->0}[f(x)(1+|sinx|)-f(0)]/x=lim{x->0}[f(x)-f(0)](1+|sinx|)/x+lim{x->0}[f(0)(1+|sinx|)-f(0)]/x=f'(0)+lim{x->0}f(0)|sinx|/x左极限lim{x->0-}f(0)|sinx|/x=-f(0),右极限lim{x->0+}f(0)|sinx|/x=f(0)...