Evaluate : `lim_(xrarr0) (sqrt(1+x)-sqrt(1-x))/( x)`

Explanation

`underset(xrarr0)"lim" (sqrt(1+x)-sqrt(1-x))/(x)`
`=underset(xrarr0)"lim"(sqrt(1+x)-sqrt(1-x))/(x)xx(sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))`
`=underset(xrarr0)"lim"((1+x)-(1-x))/(x(sqrt(1+x)+sqrt(1-x)))`
`=underset(xrarr0)"lim"(2)/(sqrt(1+x)+sqrt(1-x))`
`=(2)/(sqrt(1)+sqrt(1))=(2)/(2)=1`.