Evaluate: `lim_(xrarr0) ((3+x)^(1//2)-(3-x)^(1//2))/(x)`

Explanation

` underset(xrarr0)"lim"((3+x)^(1//2)-(3-x)^(1//2))/(x)`
`=underset(xrarr0)"lim"(sqrt(3+x)^(1//2)-(3-x)^(1//2))/(x)xx(sqrt(3+x)+sqrt(3-x))/(sqrt(3+x)+sqrt(3-x))`
`=underset(xrarr0)"lim"(2x)/(x(sqrt(3+x)+sqrt(3-x)))`
`underset(xrarr0)"lim"(2x)/(sqrt(3+x)+sqrt(3-x))`
`=(2)/(sqrt(3)+sqrt(3))=(1)/sqrt(3)`