Answer
$\infty $
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {5x^{2}+2}{\sqrt {x^{2}+3}}=\dfrac {5x^{2}+2}{\sqrt {x^{2}\left( 1+\dfrac {3}{x^{2}}\right) }}=\dfrac {5x^{2}+2}{x\sqrt {\left( 1+\dfrac {3}{x^{2}}\right) }}=\dfrac {5x+\dfrac {2}{x}}{\sqrt {1+\dfrac {3}{x^{2}}}}=\dfrac {5x+0}{\sqrt {1+0}}=5x=\infty $
