Question

$\underset{x\to a}{lim}\frac{x^{\frac{5}{8}}-a^{\frac{5}{8}}}{x^{\frac{1}{3}}-a^{\frac{1}{3}}}=$

• A. $\frac{15}{8}{a}^{\frac{7}{24}}$
• B. $\frac{15}{4}{a}^{\frac{7}{24}}$
• C. $-\frac{15}{8}{a}^{\frac{7}{24}}$
• D. $\frac{15}{4}{a}^{-\frac{7}{24}}$

Answer 1

The correct option is A $\frac{15}{8}{a}^{\frac{7}{24}}$

At $x=a$ numerator and denominator becomes zero.

Using L-Hospital's rule, we get:
$={lim}_{x\to a}\frac{\left[\right(5/8\left)x^{-3/8}\right]}{\left[\right(1/3\left)x^{-2/3}\right]}$

$=\left(15/8\right)a^{7/24}$