limit as x goes to infinite of:

sqrt(x^2 + x + 1) - sqrt(x^2 -x)

If you multiply top and bottom by sqrt(x^2 + x + 1) + sqrt(x^2 -x) then it simplifies to:

(2x+1) / [sqrt(x^2 + x + 1) + sqrt(x^2 -x)]

Then you can plug in infinite and it comes to infinite/infinite which means you can use l'hospital's rule. I'm stuck there because the rule doesn't seem to be working. Any help would be greatly appreciated as I am .

 

Just using your summary, wouldn't the answer be 1? Anything over itself equals 1. It's been a long time, so forgive me if I'm being naive!

 

Normally yes that's the case but there a bunch of rules in math concerning indeterminant forms and these include infinite/infinite, 0/0, 0^infinite, and things like that. Thanks for trying though. I've made dumber mistakes but this time I think I've done it right thus far...just can't figure out the rest.

 

The answer is actually 1. You can graph that equation on a graphing calculator and see that.

It's been too long for me to actually remember how to prove it though.

Sorry.

 

Yeah I'm all set. I posted in regular lounge at same time and a genius from Texas A&M hooked me up .