Question

If $\rm \displaystyle \lim_{x\to a}\ \frac{x^{9}-a^{9}}{x-a}=9$, find all possible values of a.

Answer 1

Solution :


$\rm \displaystyle \lim_{x\to a}\ \frac{x^{9}-a^{9}}{x-a}=9$

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We know that ,

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

= n× $a^{(n-1)}$

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=>9 × $a^{(9-1)}$ = 9

=> 9$a^{8}$ = 9

=> $a^{8}$ = 9/9

=> $a^{8}$ = 1

=> a = 1

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