_ x 0 (1 + x) ^n - 1 x = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^n} - 1}}{x} = $

✓
$n$
B
$1$
C
$-1$
D
None of these

✓

Answer

Correct option: A.

$n$

a
(a) $\mathop {\lim }\limits_{x \to 0} \,\frac{{(1 + nx + {\,^n}{C_2}{x^2} + ...{\rm{higher powers of }}x{\rm{ to }}{x^n}) - 1}}{x} = n$.

Aliter : Apply $ L-$ Hospital’s rule.

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