If _ x 2 x^n - 2^n x - 2 = 80, where n is a positive integer, the… - Vidyadip

MCQ

If $\mathop {\lim }\limits_{x \to 2} \frac{{{x^n} - {2^n}}}{{x - 2}} = 80$, where $n$ is a positive integer, then $n = $

A
$3$
✓
$5$
C
$2$
D
None of these

✓

Answer

Correct option: B.

$5$

b
(b) $\mathop {\lim }\limits_{x \to 2} \,\,\frac{{{x^n} - {2^n}}}{{x - 2}} = n\,.\,{2^{n - 1}}\,\, $

$\Rightarrow \,\,n.\,{2^{n - 1}} = 80\,\, \Rightarrow \,\,n = 5$.

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