Choose the correct answer. _ x 0 (1+x)^ n -1 x is equal to: - Vidyadip

MCQ

Choose the correct answer. $\lim\limits_{\text{x} \rightarrow0}\frac{(1+\text{x})^{\text{n}}-1}{\text{x}}$ is equal to:

✓
$\text{n}$
B
$1 $
C
$-\text{n}$
D
$0$

✓

Answer

Correct option: A.

$\text{n}$

Given $\lim\limits_{\text{x} \rightarrow 0}\frac{(1+\text{x})^{\text{n}}-1}{\text{x}}=\lim\limits_{\text{x} \rightarrow 0}\frac{(1+\text{x})^{\text{n}}-(1)^{\text{n}}}{(1+\text{x})-(1)}$
$=\lim\limits_{\text{x} \rightarrow 0}\frac{(1+\text{x})^{\text{n}}-(1)^{\text{n}}}{1+\text{x}-(2)}=\text{n}(1)^{\text{n}-1}$
$=\text{n}$

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