Question

Evaluate ${lim}_{x\to a}\frac{x^{5/7}-a^{5/7}}{x^{2/7}-a^{2/7}}$

Answer 1

We have,

${lim}_{x\to a}\frac{x^{\frac{5}{7}}-a^{\frac{5}{7}}}{x^{\frac{2}{7}}-a^{\frac{2}{7}}}$

Apply L-hospital rule,

${lim}_{x\to a}\frac{\frac{5}{7}{x}^{\frac{-2}{7}}-0}{\frac{2}{7}{x}^{\frac{-5}{7}}-0}={lim}_{x\to a}\frac{5}{2}{x}^{\frac{3}{7}}=\frac{5}{2}{\left(a\right)}^{\frac{3}{7}}$

Hence, this is the answer.