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lim(xrarr0)((1+x)^(n)-1)/(x) is equal to...

`lim_(xrarr0)((1+x)^(n)-1)/(x)` is equal to

A

n

B

1

C

`-n`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `lim_(xto0)((1+x)^(n)-1)/(x) = lim_(xto0)((1+x)^(n)-1)/((1+x)-1)=lim_(xto0)((1+x)^(n)-1)/((1+x)-1)`
`lim_(xto0)((1+x)^(n)-1^(n))/((1+x)-1)=lim_((1+x)to1)((1+x)^(n)-1^(n))/((1+x)-1)`
`=n.(1)^(n-1)=n` `[therefore lim_(xtoa)(x^(n)-a^(n))/(x-a) = na^(n-1)]`
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