If _ x a x^9 + a^9 x + a = 9, then a = - Vidyadip

MCQ

If $\mathop {\lim }\limits_{x \to a} \frac{{{x^9} + {a^9}}}{{x + a}} = 9$, then $a = $

✓
${9^{1/8}}$
B
$ \pm 2$
C
$ \pm 3$
D
None of these

✓

Answer

Correct option: A.

${9^{1/8}}$

a
$(a)$ $\mathop {\lim }\limits_{x \to a} \,\frac{{{x^9} + {a^9}}}{{x + a}} = 9\,\, $

$\Rightarrow \,\,\frac{{2{a^9}}}{{2a}} = 9\,\, \Rightarrow \,\,{a^8} = 9$

$ \Rightarrow \,\,\,\,a = {9^{1/8}}$

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