limit

[man111]

A twice differentiable function satisfy [tex]x+f(x)\cdot f'(x)+f'(x)\cdot f''(x)=0.[/tex] Then

[tex](1)\lim_{x\rightarrow 0}x\cdot f(x)=[/tex]

[tex](2)\lim_{x\rightarrow 0}x\cdot f(x)\cdot f'(x)=[/tex]

[tex](3)\displaystyle \lim_{x\rightarrow 0}\frac{f'(x)}{\ln|x|}=[/tex]

[tex](4)\displaystyle \lim_{x\rightarrow 0}\frac{f'(x)f'(x)}{\ln|x|}=[/tex]