$=\mathop {\lim }\limits_{x \to 0}\frac{x^{2}\sqrt{1+2x}}{x(4x+5)}+\mathop {\lim }\limits_{x \to 0}\frac{2014(\sqrt{1+2x}-1)}{x(4x+5)}$$=\mathop {\lim }\limits_{x \to 0}\frac{x\sqrt{1+2x}}{4x+5}+\mathop {\lim }\limits_{x \to 0}\frac{2014(1+2x-1)}{x(4x+5)(\sqrt{1+2x}+1)}$
$=0 + \mathop {\lim }\limits_{x \to 0}\frac{4028x}{x(4x+5)(\sqrt{1+2x}+1)}$
$=\mathop {\lim }\limits_{x \to 0}\frac{4028}{(4x+5)(\sqrt{1+2x}+1)}=\frac{4028}{5.2}=402,5$