Evaluate `lim_(x to 0) (sqrt(x + 2) - sqrt(2))/(x)`

Explanation

We have `underset(x to 0)(lim) (sqrt(x + 2) - sqrt(2))/(x)`
Let `x + 2 = y` so as `x to 0, y to 2`
`underset(x to 0)(lim) (sqrt(x + 2) - sqrt(2))/(x) underset(x to 2)(lim) (sqrt(y) - sqrt(2))/(y - 2) = underset( y to 0)(lim) (y^(1//2) - 2^(1//2))/( y - 2) = (1)/(2) (2)^(1//2 - 1) = (1)/(2) (2)^(-1//2) = (1)/(2sqrt(2))`