Evaluate the following limit: `underset( x rarr 0) ( "lim")(sqrt(1+x^2)-sqrt(1-x^2))/x`

Explanation

`(lim)_(x->0)(sqrt(1+x^2)-sqrt(1-x^2))/x`


L'Hopital Rule:


`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`


`(lim)_(x->0) x/sqrt(1+x^2)+x/sqrt(1-x^2)`


`=0/sqrt(1+0^2)+0/sqrt(1-0^2)=0+0=0`