Ta có: `(\sqrt{1+4x}-1)/(x)=((\sqrt{1+4x}-1)(\sqrt{1+4x}+1))/(x(\sqrt{1+4x}+1))=(1+4x-1)/(x(\sqrt{1+4x}+1))=(4)/((\sqrt{1+4x}+1)`

$\rightarrow$ $\lim\limits_{x \to 0^+} f(x)=\lim\limits_{x \to 0}$ `(4)/(\sqrt{1+4x}+1)=(4)/(\sqrt{1+4.0}+1)=2`

$\lim\limits_{x \to 0^-} f(x)=\lim\limits_{x \to 0^-}$ `[m(x+2)-1]=m(0+2)-1=2m-1`

$\exists$ $\lim\limits_{x \to 0} f(x)$ khi `2=2m-1` $\rightarrow$ `m=(3)/(2)`