3.设f(x)在 =O 的邻域内二阶可导,且 '(0)=0,-|||-''(0)=2, 求-|||-lim _(xarrow 0)dfrac (f(x)-f[ ln (1+x)] )({x)^3} .

四、设函数 y=f(x) 的二阶可导,且 (x)gt 0 (0)=0, (0)=0, 求-|||-lim _(xarrow 0)dfrac ({x)^3f(u)

[例15]设f(x)连续可导,且 lim _(xarrow 0)([ 1+x+dfrac {f(x))(x)] }^dfrac (1{x)}=(e)^3, 求f

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)=(

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

设y=f(x) 在x0处可导,且 ((x)_(0))=2, 则lim _(xarrow 0)dfrac (f({x)_(0)+2)x-f((x)_(0)-f(x

设函数f(x)二阶可导,f(x)是f(x)+2f(x)+e^x的一个原函数,且f(0)=0.f(0)=1求f(x),设函数f(x)二阶可导,f'(x)是f'(x

设f(x)在[0,1]上连续,在(0,1)内二阶可导,且f^1/2[f(x)-x]dx= f(0), (1)=0,证明:(1)存在f^1/2[f(x)-x]dx

1.设f(x)具有二阶连续导数,且 (0)=0, lim _(xarrow 0)dfrac ({f)^n(x)}(|x|)=1, 则 () .-|||-(A)f

[题目]设f(x )具有二阶连续导数,且f(0)-|||-=0, lim _(xarrow 0)dfrac (f(x))(|x|)=1 则 ()-|||-A.f

设函数f(x)在 x=0 的某个邻域内有连续的二阶导-|||-数,且 (0)=f(0)=0, 则 __-|||-(A) x=0 必是f(x)的零点-|||-(B