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What is lim(xto0) (sqrt(1+x-1))/(x)...

What is `lim_(xto0) (sqrt(1+x-1))/(x)`

A

0

B

`(1)/sqrt(2)`

C

1

D

`-(1)/sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xto0)lim(sqrt(1+x-1))/(x)`
`=underset(xto0)lim(sqrt(1+x-1))/(x)xx(sqrt(1+x+1))/(sqrt(1+x+1))=underset(xto0)lim(1+x-1)/(x[sqrt(1+x+1)])`
`=underset(xto0)lim(1)/(sqrt(1+x+1))=(1)/(sqrt(1+0+1))=(1)/sqrt(2)`
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