Reply to thread

Message

<blockquote data-quote="HomerSimpson" data-source="post: 1428660" data-attributes="member: 259463">Need: limit as x -&gt; infinity of [sqrt(x^2 - x) - sqrt(x^2 - x - 2)]Clearly the limit is zero since the -2 will become insignificant as x becomes very large. But i&#039;d like to answer the question without this explanation (i know its valid but still seems dodgy to me).I changed sqrt(x^2 - x) - sqrt(x^2 - x - 2) to {sqrt(x^2 - x)} * {1 - sqrt[1 - 2/(x^ - x)]}So then the term 2/(x^ - x) approaches 0 as x approaches infinity. And so {1 - sqrt[1 - 2/(x^ - x)]} would become 1-1=0. But then as x approaches infinity {sqrt(x^2 - x)} approaches infinity. So then we have infinity*0, which is undefined. So then this method doesn&#039;t seem to give me a definite answer. Can someone point out any mistakes and show how i can use this method to show clearly and definitely that the limit is zero or provide another method which will allow me to do so.</blockquote>

[QUOTE="HomerSimpson, post: 1428660, member: 259463"] Need: limit as x -> infinity of [sqrt(x^2 - x) - sqrt(x^2 - x - 2)] Clearly the limit is zero since the -2 will become insignificant as x becomes very large. But i'd like to answer the question without this explanation (i know its valid but still seems dodgy to me). I changed sqrt(x^2 - x) - sqrt(x^2 - x - 2) to {sqrt(x^2 - x)} * {1 - sqrt[1 - 2/(x^ - x)]} So then the term 2/(x^ - x) approaches 0 as x approaches infinity. And so {1 - sqrt[1 - 2/(x^ - x)]} would become 1-1=0. But then as x approaches infinity {sqrt(x^2 - x)} approaches infinity. So then we have infinity*0, which is undefined. So then this method doesn't seem to give me a definite answer. Can someone point out any mistakes and show how i can use this method to show clearly and definitely that the limit is zero or provide another method which will allow me to do so. [/QUOTE]

Name

Verification

Loading…