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L'hospitals

mathslover786

fanx

(edited 12 years ago)

What limit are you evalutating? and why you need to use L'hospital rule?

Reply 3

username165864

Original post by mathslover786

why cant you use L'hospitals rule on this:

(3·x + 1)^0.5 / (x + 1)^0.5?

Whatever the limit, L'Hopital's Rule is only valid for cases where you have (when you evaluate the limit on the numerator and denominator):

\frac{0}{0}

\frac{\infty}{\infty}

More formally, L'Hopital's Rule requires the following conditions to be true:

Let

\text{f,g:}\ [a,b) \to \Re

be continuous and differentiable functions on (a,b).

Suppose the following conditions hold:
(1)

g'(x) \not= 0

for all x in (a,b).
(2) f(a) = 0 = g(a)
(3)

\displaystyle \lim_{x \to a} \frac {f'(x)}{g'(x)} \ \text{exists.}

Then,

\displaystyle \lim_{x \to a} \frac {f(x)}{g(x)} = \lim_{x \to a} \frac {f'(x)}{g'(x)}

NOTE:

\Re

denotes the real set. Also, all limits are in fact meant to be limits from above only, but the limitations of LaTeX does not allow this.

If any part of this definition is not true, then L'Hopital's Rule fails. Substitute in your f,g into this definition.

Reply 4

You Failed

L'hospitals rule?

I lol'ed.

Reply 5

username165864

Original post by You Failed

L'hospitals rule?

I lol'ed.

Hôpital is French for Hospital, and thus some textbooks (and in America) the name L'Hospital's Rule is used. It's really not that hilarious...

Reply 6

You Failed

Original post by Mathematician!

Hôpital is French for Hospital, and thus some textbooks (and in America) the name L'Hospital's Rule is used. It's really not that hilarious...

Oh!! I didn't know that... I assumed L'Hopital, was the name of a mathematician and thus wouldn't translate...

EDIT: Ok, my assumption was right. Do they really translate names like that? =/

Reply 7

davros

Original post by You Failed

Oh!! I didn't know that... I assumed L'Hopital, was the name of a mathematician and thus wouldn't translate...

EDIT: Ok, my assumption was right. Do they really translate names like that? =/

l'Hospital is the original spelling and is technically correct. The circumflex didn't come into use in French until much later and usually indicates the omission of a consonant (e.g. 's') after a vowel.

Reply 8

Ewan

Original post by You Failed

L'hospitals rule?

I lol'ed.

Whether technically correct or not, I still lol'ed :teehee:

Reply 9

G550NDH

I agree hospitals do rule

Reply 10

You Failed

Original post by davros

Mm, interesting. I still don't quite get it though. A name is a name. You don't say "Well Dave used to be called David, so let's call him David even though his name is Dave". You're probably right, I know but as a personal opinion, I don't think people's names should be changed or translated, I think they should remain the same. If he was called L'Hopital, it should stay that way. Not to mention, L'Hospital, just sounds kinda weird =P