lim{√[(x+p)(x+q)] - x}
=lim{√[(x+p)(x+q)] - x} * {√[(x+p)(x+q)] + x}/{√[(x+p)(x+q)] + x}
=lim[(x+p)(x+q) - x^2]/{√[(x+p)(x+q)] + x}
=lim[(p+q)*x + pq]/{√(x+p)(x+q)] + x}
=lim[(p+q) + pq/x]/{√[(1+p/x)(1+q/x)] + 1} 注:分子、分母同除以 x
=lim[(p+q) + 0]/{√[(1+0)(1+0)] + 1]}
=(p+q)/2