Evaluate $\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^3-8}{x^2-4}}$

The limit of the quotient of $x$ cubed minus $8$ by $x$ squared minus $4$ as the value of $x$ approaches $2$ is written in the following mathematical form.

$\displaystyle \large \lim_{x\,\to\,2}{\normalsize \dfrac{x^3-8}{x^2-4}}$

According to the direct substitution method, let’s find the limit of the $x$ cube minus $8$ by $x$ square minus $4$ as the value of $x$ approaches $2$.

$=\,\,\,$ $\dfrac{2^3-8}{2^2-4}$

$=\,\,\,$ $\dfrac{8-8}{4-4}$

$=\,\,\,$ $\dfrac{0}{0}$

The limit of the rational function $x$ cubed minus $8$ by $x$ squared minus $4$ is indeterminate as the value of $x$ is closer to $2$. It clears that the direct substitution method is not useful to find the limit for the given rational function.

Factorization

Learn how to find the limit of the quotient of $x$ cube minus $8$ by $x$ square minus $4$ as $x$ approaches $0$ by using factorization or factorisation method.

Formulas

Learn how to calculate the limit of the quotient of $x$ cubed minus $8$ by $x$ squared minus $4$ as $x$ is closer to $0$ by using formulas.

L’Hôpital’s Rule

Learn how to calculate the limit of the quotient of $x$ cubed minus $8$ by $x$ squared minus $4$ as $x$ is closer to $0$ by using formulas.

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