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

Explanation

Given that limit: `lim_(x->0)(sqrt(1+x+x^2)-sqrt(x+1))/(2x^2)`
`l = lim_(x->0)(sqrt(1+x+x^2)-sqrt(x+1))/(2x^2)xx(sqrt(1+x+x^2)+sqrt(x+1))/ (sqrt(1+x+x^2)+sqrt(x+1))`
`l=lim_(x->0) (1+x+x^2-x-1)/((2x^2)(sqrt(1+x+x^2)+sqrt(x+1)))`
`l=1/2(2)`
`l=1/4`