Answer
$\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}=-5$
Work Step by Step
$\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}$
Take out common factor $x^{2}$ in the numerator and simplify:
$\lim\limits_{x \to 0}\dfrac{x^{4}-5x^{2}}{x^{2}}=\lim\limits_{x \to 0}\dfrac{x^{2}(x^{2}-5)}{x^{2}}=\lim\limits_{x \to 0}x^{2}-5=...$
Apply direct substitution to evaluate the limit:
$\lim\limits_{x \to 0}x^{2}-5=(0)^{2}-5=-5$
