f(x)在 [ -8,8] 上有定义, (0)=1, 且满足-|||-lim _(xarrow 0)dfrac (ln (1-2x)+2xf(x))({x)^2}=0-|||-证明:f(x)在 x=0 处可导,并求 f`(0).

设f(x)在R上有定义, (0)=1, 且满足:-|||-lim _(xarrow 0)dfrac (ln (1-2x)+2xf(x))({x)^2}=0-||

2.设f(x)在 x=0 的邻域内有定义, (0)=1, 且 lim _(xarrow 0)dfrac (ln (1+2x)-2xf(x))({x)^2}=0-

(2)设函数f(x)在区间 (-1,1) 内有定义,且 lim _(xarrow 0)f(x)=0, 则-|||-(A)当 lim _(xarrow 0)dfr

设 函数 f ( x ) 在 x = 0 处可导，且lim _(xarrow 0)dfrac (f(2x)-f(0))(ln (1+3x))=1，则f(0)=(

[问答题]设函数f（x）满足f（x＋Δx）－f（x）＝2xf（x）Δx＋o（Δx）（Δx→0），且f（0）＝2，则f（1）＝_________

已知f(x)满足 lim _(xarrow 1)dfrac (f(x))(ln x)=1, 则 () .-|||-(A) f(1)=0 (B) lim _(xa

设lim _(xarrow 0)dfrac (ln (1+x+dfrac {f(x))(x))}(x)=3，则lim _(xarrow 0)dfrac (ln

设f(x)可导,且满足 lim _(xarrow 0)dfrac (f(1)-f(1-2x))(x)=-2, 则曲线 =f(x) 在点(1,f(1))处的切线斜

2.设函数f(x)在区间 (-1,1) 内有定义,且 lim _(xarrow 0)f(x)=0, 则 ()-|||-A.当 lim _(xarrow 0)df

已知 lim _(xarrow 0)([ 1+x+dfrac {f(x))(x)] }^dfrac (1{x)}=(e)^3, 则 lim _(xarrow 0