$L=\mathop {\lim }\limits_{x \to 0} \frac{\sqrt{2x+1}-\sqrt[3]{x^2+1} }{x}$
$L=\mathop {\lim }\limits_{x \to 0} \frac{\sqrt{2x+1}-1 }{x}-\mathop {\lim }\limits_{x \to 0} \frac{\sqrt[3]{x^2+1}-1 }{x}$
$L=\mathop {\lim }\limits_{x \to 0} \frac{2 }{\sqrt{2x+1}+1 }-\mathop {\lim }\limits_{x \to 0} \frac{x}{\sqrt[3]{(x^2+1)^2}+\sqrt[3]{x^2+1}+1}$
$L=\frac{2}{2}+0=1.$