Question

Evaluate
$\rm \displaystyle \lim_{x\to a}\ \frac{x^{5/7}-a^{5/7}}{x^{2/7}-a^{2/7}}$

Answer 1

Solution :

$\rm \displaystyle \lim_{x\to a}\ \frac{x^{5/7}-a^{5/7}}{x^{2/7}-a^{2/7}}$

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We know that ,

$\rm \displaystyle \lim_{x\to a}\ \frac{x^{m}-a^{m}}{x^{n}-a^{n}}$

= (m/n)×$a^{(m-n)}$

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= (5/7)/(2/7) ×$a^{(5/7-2/7)}$

= 5/2 × $a^{(3/7)}$

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