lim(x趋向正无穷)根号[(x+p)(x+q)]-x怎么做?

题目

lim(x趋向正无穷)根号[(x+p)(x+q)]-x怎么做?

答案

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