Question

The value of $\displaystyle \lim_{x \to 3} \frac{x^{5}-3^{5}}{x^{8}-3^{8}}$ is equal to

• A. $\frac{5}{8}$
• B. $\frac{5}{64}$
• C. $\frac{5}{216}$
• D. $\frac{1}{27}$

Answer 1

Answer: (C)

$\frac{5}{216}$

Answer 2

$\lim\limits _{x \rightarrow 3} \frac{x^{5}-3^{5}}{x^{8}-3^{8}} \,\,\,\left(\right.$ form $\left.\frac{0}{0}\right)$
$=\lim\limits _{x \rightarrow 3} \frac{5 x^{4}}{8 x^{7}} \,\,\,$ (L'Hospital's rule)
$=\lim \limits_{x \rightarrow 3} \frac{5}{8 x^{3}}=\frac{5}{8 \times 3^{3}}=\frac{5}{8 \times 27}=\frac{5}{216}$