分子有理化呀
lim(x→∞)[{√(x+p)(x+q)}-x]
=lim(x→∞)[{√(x+p)(x+q)}-x])[{√(x+p)(x+q)}+x]/[{√(x+p)(x+q)}+x]
=lim(x→∞)[(p+q)x+pq]/[{√(x+p)(x+q)}+x]
=lim(x→∞)[(p+q)x+p1]/(2x)
=(p+q)/2
分子有理化呀
lim(x→∞)[{√(x+p)(x+q)}-x]
=lim(x→∞)[{√(x+p)(x+q)}-x])[{√(x+p)(x+q)}+x]/[{√(x+p)(x+q)}+x]
=lim(x→∞)[(p+q)x+pq]/[{√(x+p)(x+q)}+x]
=lim(x→∞)[(p+q)x+p1]/(2x)
=(p+q)/2