6 tutors & still can't solve a limit problem (calculus)

[PowerMacG5]

Originally posted by: JohnCU

Originally posted by: Marauder911

Originally posted by: JohnCU

Originally posted by: Marauder911
I am not going to help you simply for the egregious error of continuing to say "L'Hospital" after numerous people said "L'Hopital."

Um, that's the correct way to spell it.

Uhm, It's L'Hopital, not L'Hospital.

I guess my book and my teacher spell it wrong then.

Check your notes because everything my book, and teacher say spell it L'Hôpital.

 

[BigJ]

Originally posted by: JohnCU

Originally posted by: Marauder911

Originally posted by: JohnCU

Originally posted by: Marauder911
I am not going to help you simply for the egregious error of continuing to say "L'Hospital" after numerous people said "L'Hopital."

Um, that's the correct way to spell it.

Uhm, It's L'Hopital, not L'Hospital.

I guess my book and my teacher spell it wrong then.

I think both ways are acceptable. I've seen it spelt more often without the s though.

EDIT:
L'Hospital's Rule

This result first appeared in l'Hospital's 1696 treatise, which was the first text book on differential calculus. Note that l'Hospital's name is commonly seen spelled both "l'Hospital" (e.g., Maurer 1981, p. 426; Arfken 1985, p. 310) and "l'Hôpital" (e.g., Maurer 1981, p. 426; Gray 1997, p. 529), the two being equivalent in French spelling

 

[RaynorWolfcastle]

Originally posted by: JohnCU

Originally posted by: Marauder911
I am not going to help you simply for the egregious error of continuing to say "L'Hospital" after numerous people said "L'Hopital."

Um, that's the correct way to spell it.

JohnCU is correct, I just checked my Larousse (French) dictionary and even they spell it L'Hospital.

 

[JohnCU]

Originally posted by: Marauder911
Check your notes because everything my book, and teacher say spell it L'Hôpital.

I've got it right here infront of my face. Calculus - James Stewart 5th edition - "L'Hospital's Rule"

 

[BigJ]

Guys, see my post above.

 

[BehindEnemyLines]

Originally posted by: RaynorWolfcastle
ok, I'll post the solution, give me a minute to type it out.

OK here it is, the longwinded way:
y = limit(500*(1+.05/x)^10x)
y/500 = limit(1+.05/x)^10x
ln(y/500) = limit(10x*ln(1+.05/x)) => 0*infinity so we rewrite
ln(y/500) = limit(ln[(1+.05/x)/(1/10x)] => 0/0 so we use l'hopital I'll skip the limit() on the steps below for convenience
= 1/(1+.05/x)*(-.05/x^2) / (-1/10x^2)
we rewrite the numerator as 1/(x(20x+1) and cancel the negative signs to get
= [1/(x(20x+1)] / [1/10x^2] which we can now rewrite in a more readable form
= 10x^2/[x(20x+1)]
= 10x/(20x+1), this limit as x -> infinity is easy
= 1/2

so now we have
ln(y/500) = 1/2
which we rewrite as
y = 500*sqrt(e) ~=824

Your tutors suck for not figuring it out btw.

Thanks a lot. I'll verify that when I get home from the Math Learning Center. I've asked all the tutors there, and none of them could figure it out. Most of the tutors are students (with a few who have degrees in mathmetics, but they're aren't available). I've been here doing that problem since 1:30pm plus last night. Maybe now I can be a little more sane.

 

[PowerMacG5]

Originally posted by: JohnCU

Originally posted by: Marauder911
Check your notes because everything my book, and teacher say spell it L'Hôpital.

I've got it right here infront of my face. Calculus - James Stewart 5th edition - "L'Hospital's Rule"

And I have my text - Calculus: 7th Edition by Anton, Bivens, and Davis - in front of me, "L'Hôpital's rule", p. 500. I guess BigJ is correct in both ways being acceptable.

 

[BehindEnemyLines]

Originally posted by: BigJ

Originally posted by: JohnCU

Originally posted by: Marauder911

Originally posted by: JohnCU

Originally posted by: Marauder911
I am not going to help you simply for the egregious error of continuing to say "L'Hospital" after numerous people said "L'Hopital."

Um, that's the correct way to spell it.

Uhm, It's L'Hopital, not L'Hospital.

I guess my book and my teacher spell it wrong then.

I think both ways are acceptable. I've seen it spelt more often without the s though.

EDIT:
L'Hospital's Rule

This result first appeared in l'Hospital's 1696 treatise, which was the first text book on differential calculus. Note that l'Hospital's name is commonly seen spelled both "l'Hospital" (e.g., Maurer 1981, p. 426; Arfken 1985, p. 310) and "l'Hôpital" (e.g., Maurer 1981, p. 426; Gray 1997, p. 529), the two being equivalent in French spelling

My James Stewart 5th Ed. Calculus book spells it as L'Hospital's Rule.

 

[RaynorWolfcastle]

FYI, L'Hospital and L'Hopital aren't equivalent in French. "hôpital" translates to hospital, but "hospital" is not a widely accepted spelling of the word (in French, that is). Nonetheless, the correct name is L'Hospital, but I guess some authors thought it was a typo or something and tried to correct the name to what they figured was the correct name in French.

The point is, if the Larousse dictionary writes it L'Hospital and doesn't make reference to any other spelling, you can be fairly certain that it is the only correct way to spell it.

 

[Kyteland]

Originally posted by: BehindEnemyLines
My James Stewart 5th Ed. Calculus book spells it as L'Hospital's Rule.

5th Ed.?!? Already? I used the 3rd in college, 4 years ago. I can hardly believe they put out 2 more editions in that time.....

 

[Goosemaster]

Originally posted by: RaynorWolfcastle
Your tutors suck for not figuring it out btw.

Yes, and ridiculously so. This is a VERY importatn problem, and every calc teacher I know emphasizes this type of problem, including through placement on a test.

I'll admit I make mistakes as a tutor, but damn.

 

[BehindEnemyLines]

Thanks everyone for the help, especially RaynorWolfcastle for the steps-by-steps. I guess the tutors (and myself) made it harder than it was. Now, I need to do Improper Integrals.... :roll:.

And yes, it's ridiculus they come a new edition every year or so. My college actually started using the new edition just Fall of 2003. I got mine for about $76 from Amazon.com. The college bookstore sells it for $110 (used) and $130 (new) - the highest markup price in the district :shocked: . They recently stopped using the Thomas something.

 

[TuxDave]

Then there's the super cheating method to do this. There's an identity you can use.

(1+1/x)^x as x---> infinity = e

So... here's the easy way, but I guess not the way your teacher wants it.

500(1+0.05/x)^10x lim x-->infinity: let y = x/0.05
500(1+1/y)^0.5y lim y--> infinity
500{(1+1/y)^y}^0.5 lim y--> infinity
500*sqrt(e)

:-D

The identity is quickly derived by:

y = lim[(1+1/x)^x]
ln(y) = lim[xln(1+1/x)] = lim[ln(1+1/x)/{1/x}]
***l'hospital
ln(y) = 1/(1+1/x) = 1
y = e