tough limit problem

mikau · 2006-09-11 11:58:49

Find the limit without using L'hopitals rule.

limit of sqrt (x^2 + x + 1) + x as x approaches negative infinity.

I've been playing with it for about an hour to no avail. :-(

John E. Franklin · 2006-09-12 10:54:59

I guess the limit is negative one-half, but I may not be exactly right.

My logic is that 7.5 x 7.5 is 56.25 and 7x8 is 56.

mikau · 2006-09-12 14:42:18

The answer is 1/2 or -1/2, I don't remember. I'd just like to know how did they find it.

Ricky · 2006-09-12 16:14:44

-1/2, although I'm as stumped as you are.

numen · 2006-09-12 20:49:49

I don't know what L'hopitals rule is, but here's what I did (hoping that I didn't use it!):

Ricky · 2006-09-13 02:54:20

If you don't know L'H rule, then you can be sure that you didn't use it. L'H rule is:

If f(x) goes to 0 and g(x) goes to 0 as x goes to c, then:

numen · 2006-09-13 03:21:19

It's not even in my calculus textbook.

Ricky · 2006-09-13 05:58:30

I can just about guarantee you that it is. The equivalent would be writing a calculus text book and forgetting to talk about Riemann sums.

mikau · 2006-09-14 13:11:20

Ricky, doesn't L'hopitals rule only apply if it is in an indeterminant form such as 0/0 or infinity/infinity?

Ricky · 2006-09-14 14:26:10

Yes, infinity/infinity works as well.

mikau · 2006-09-14 15:19:49

yes but I thought it ONLY worked in that case. Not true?

Ricky · 2006-09-14 17:30:54

I'm starting to get the feeling you missed the line that I wrote:

If f(x) goes to 0 and g(x) goes to 0 as x goes to c, then:

But yes, it must be that f(x) and g(x) both go to 0 or +/- infinity.

mikau · 2006-09-15 03:52:19

ok, right.

mikau · 2006-09-15 07:54:09

If you don't know L'H rule, then you can be sure that you didn't use it.

Not true! I think what he meant was he's not familiar what "L'hopitals rule" refers to so he wouldn't know if he was using it. Just like a lot of people forget the transiative and associative property are, but they use them every day. You know the property, but forget the name.

Anyway, thanks Numen for the solution. you often forget you can factor out an x in an expression like x + 1. That also causes the appearance of terms like 1/x^n which are valuable in limit problems. Thanks again!

Last edited by mikau (2006-09-15 07:56:34)

numen · 2006-09-15 08:26:09

No problem : )

Ricky · 2006-09-15 12:05:44

Right mikau. And what I meant was that it's not like commutative or associative laws. If you don't know what L'H rule is, then you won't use it by accident, because it's not a common sense rule.

mikau · 2006-09-16 02:21:10

Right right. But there are still a few theorems and laws I've forgotten the names of but still use. But yeah I know what you mean.

Math Is Fun Forum

#1 2006-09-11 11:58:49

tough limit problem

#2 2006-09-12 10:54:59

Re: tough limit problem

#3 2006-09-12 14:42:18

Re: tough limit problem

#4 2006-09-12 16:14:44

Re: tough limit problem

#5 2006-09-12 20:49:49

Re: tough limit problem

#6 2006-09-13 02:54:20

Re: tough limit problem

#7 2006-09-13 03:21:19

Re: tough limit problem

#8 2006-09-13 05:58:30

Re: tough limit problem

#9 2006-09-14 13:11:20

Re: tough limit problem

#10 2006-09-14 14:26:10

Re: tough limit problem

#11 2006-09-14 15:19:49

Re: tough limit problem

#12 2006-09-14 17:30:54

Re: tough limit problem

#13 2006-09-15 03:52:19

Re: tough limit problem

#14 2006-09-15 07:54:09

Re: tough limit problem

#15 2006-09-15 08:26:09

Re: tough limit problem

#16 2006-09-15 12:05:44

Re: tough limit problem

#17 2006-09-16 02:21:10

Re: tough limit problem

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