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

Explanation

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


L'Hopital Rule:


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


`(lim)_(x->0)(1/sqrt(1+x)+1/sqrt(1-x))/(4)`


`=(1/sqrt(1+0)+1/sqrt(1-0))/(4)`


`=(1+1)/(4)=1/2`