The correct option is C n Consider the given function. x→ 0lim ( ( 1+x )^n 1x) #160;This is 00 form. #160;So, apply L Hospital rule, x→ ...

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Integration by Partial Fractions

limx → 01 + x...

Question

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

- n

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Solution

The correct option is C $n$
Consider the given function.

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

This is $\frac{0}{0}$ form.

So, apply L-Hospital rule,

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

$lim x \to 0 (n {(1 + x)}^{n - 1})$

$= n {(1 + 0)}^{n - 1}$

$= n$

Hence, this is the answer.

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