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→ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration by Partial Fractions

limx → 01 + x...

Question

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

- n

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

n

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Suggest Corrections

Similar questions

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

{lim}_{x \to 0} \frac{\sqrt{1 + x} - 1}{x} = {lim}_{x \to 0} \frac{(1 + x) \frac{1}{n} - 1}{(x + 1) - 1} =

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

lim x \to 1 {(\frac{x^{n} + x^{n - 1} + x^{n - 2} + . . . . + x^{2} + x - n}{x - 1})}

{lim}_{x \leftarrow 1} \frac{x + x^{2} + x^{3} + . . . . + x^{n} - n}{x - 1} =

Join BYJU'S Learning Program