Question

If $\rm \displaystyle \lim_{x\to a}\ \frac{x^{5}-a^{5}}{x-a}=405$, find all possible values of a.

Answer 1

Solution ;

$\rm \displaystyle \lim_{x\to a}\ \frac{x^{5}-a^{5}}{x-a}=405$

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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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=> 5 × $a^{(5-1)}$ = 405

=> a⁴ = 405/5

=> a⁴ = 81

=> a⁴ = 3⁴

=> a = 3

Therefore ,

a = 3

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