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Evaluate lim(xrarr0){(sqrt(1+x)-sqrt(1-...

Evaluate `lim_(xrarr0){(sqrt(1+x)-sqrt(1-x))/(x)}.`

A

`1`

B

`2`

C

`0`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`lim_(xto0){(sqrt(1+x)-sqrt(1-x))/(x)}=lim_(xto0){((sqrt(1+x)-sqrt(1-x)))/(x).((sqrt(1+x)+sqrt(1-x)))/((sqrt(1+x)+sqrt(1-x)))}`
`=lim_(xto0)({(1+x)-(1-x)})/(x(sqrt(1+x)+sqrt(1-x)))`
`=lim_(xto0)(2x)/(x(sqrt(1+x)+sqrt(1-x)))`
`=lim_(xto0)(2)/((sqrt(1+x)+sqrt(1-x)))=1" "["putting" x=0].`
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