证明:若f(x)在有限开区间(a,b )内可导,且 lim _(xarrow {a)^+}f(x)=lim _(xarrow {b)^-}f(x), 则-|||-至少存在一点 xi in (a,b), 使 '(xi )=0.

(B)若 lim _(xarrow 0)dfrac (f(x)+f(-x))(x) 存在,则 (0)=0.-|||-(C)若 lim _(xarrow 0)df

(9)已知 lim _(xarrow a)f(x)=lim _(xarrow a)g(x), 则 lim _(xarrow a)dfrac (f(x))(g(x

(B) lim f(x)=0.-|||-(C) lim _(xarrow 1)f(x)=infty . D)limf(x)不存在,且 lim _(xarrow

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

若函数f(x)在 x=0 处连续,且 lim _(xarrow 0)dfrac (f(x))(x) 存在,证明 f(x)在 x=0 处可导.

154 设 lim _(xarrow {x)_(0)^+}f(x)=lim _(xarrow {x)_(0)^-}(x)=a, 则-|||-(A)f(x)在 =

设 函数 f ( x ) 在 x = 1 处可导且lim _(xarrow 0)dfrac (f(1)-f(1-x))(2x)=1则 lim _(xarrow

1.若f(x)在 x=0 处可导,且 (0)=0, 则 lim _(xarrow 0)dfrac (f(x))(x)= __

(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f(x)二阶可导, lim _(xarrow 0)dfrac (f(x))(x)=1 (1)=1, 证明:存在 xi in (0,1), 使得-|||-(xi