Answer
$$\infty$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{{x^4}}} - \frac{1}{{{x^2}}}} \right) \cr
& {\text{evaluating the limit, we get:}} \cr
& \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{{x^4}}} - \frac{1}{{{x^2}}}} \right) = \frac{1}{{{0^4}}} - \frac{1}{{{0^2}}} \cr
& \mathop {\lim }\limits_{x \to 0} \left( {\frac{1}{{{x^4}}} - \frac{1}{{{x^2}}}} \right) = \infty - \infty \cr
& {\text{simplify }}\frac{1}{{{x^4}}} - \frac{1}{{{x^2}}} \cr
& = \mathop {\lim }\limits_{x \to 0} \left( {\frac{{1 - {x^2}}}{{{x^4}}}} \right) \cr
& {\text{evaluating the limit, we get:}} \cr
& = \frac{{1 - {{\left( 0 \right)}^2}}}{{{{\left( 0 \right)}^4}}} = \frac{1}{0}=\infty \cr
} $$
