Answer
$\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}=3$
Work Step by Step
$\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}$
Take out common factor $x$ in the numerator and simplify:
$\lim\limits_{x \to 0}\dfrac{x^{2}+3x}{x}=\lim\limits_{x \to 0}\dfrac{x(x+3)}{x}=\lim\limits_{x \to 0}x+3=...$
Apply direct substitution to evaluate the limit:
$\lim\limits_{x \to 0}x+3=0+3=3$
