设函数f(x)在点x=0处可导,且f(x)=f(0)+2x+a(x),lim a(x)/x =0(x→ 0),则f‘(0)=?

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设函数f(x)在点x=0处可导,且f(x)=f(0)+2x+a(x),lim a(x)/x =0(x→ 0),则f‘(0)=?

设函数f(x)在点x=0处可导,且f(x)=f(0)+2x+a(x),lim a(x)/x =0(x→ 0),则f‘(0)=?
设函数f(x)在点x=0处可导,且f(x)=f(0)+2x+a(x),lim a(x)/x =0(x→ 0),则f‘(0)=?

设函数f(x)在点x=0处可导,且f(x)=f(0)+2x+a(x),lim a(x)/x =0(x→ 0),则f‘(0)=?
因为lim a(x)/x =0(x→ 0) 且函数f(x)在点x=0处可导
又因为f(0)=f(0)+a(0) ,a(0)=0,
所以a'(0)=lim[ a(x)-a(0)]/(x-0),(x→ 0)=lim a(x)/x,(x→ 0)=0
f'(0)=lim[ f(x)-f(0)]/(x-0),(x→ 0)=2+lim a(x)/x,(x→ 0)=2

就是导数定义的运用

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