l'hopital's rule (1 Viewer)

[jm1234567890]

i reckon it is useful for HSC maths.

I recomend you ppl learn it.

 

[CM_Tutor]

I recommend you be VERY careful in following the above piece of advice. L'Hopital's Rule is theory beyond the Extn 2 syllabus, so you have no idea how a marker might repond to its use.

 

[hatty]

my teacher who marks 4unit in the HSC, says the markers accept it, even though its not in the silly.

 

[George W. Bush]

Curve sketcing.

 

[...]

i thought l'hopital's rule was for limits as they approach 0 or infinity where u can differentiate them...

 

[George W. Bush]

For finding limits of complicated functions as x-> 0. Let's see your pencil do that

 

[George W. Bush]

The rule is, if I recall correctly

lim x->a f(x)/g(x) = lim x-> a f'(x)/g'(x), g'x =/= 0.

 

[...]

MQ's uni lect slides

pg 13

http://www.maths.mq.edu.au/~wchen/lnfymfolder/fym07-d.pdf

 

[Affinity]

sketch x^x for positive x...

you would have to know where it tends to as x -> 0?

 

[redslert]

hmmm touched upon this when doing my hsc...
i can't remember who taught me it, i think it is most likely at my tutor becuase my school was completely crap..

anyway i never ended up using it and completely forgot about it until uni started and in calculus we were learning it

 

[jm1234567890]

remeber ONLY for 0/0 or infinity/infifnty limits

 

[t-i-m-m-y]

Originally posted by jm1234567890
remeber ONLY for 0/0 or infinity/infifnty limits

otherwise known as inderterminate forms

 

[Calculon]

Originally posted by CM_Tutor
I recommend you be VERY careful in following the above piece of advice. L'Hopital's Rule is theory beyond the Extn 2 syllabus, so you have no idea how a marker might repond to its use.

I thought you were allowed to use any methods you want as long as you dont assume any formulae etc that your not allowed to

 

[CM_Tutor]

Originally posted by Calculon
I thought you were allowed to use any methods you want as long as you dont assume any formulae etc that your not allowed to

How do you know that using L'Hopital's Rule is not assuming a formula that you're not allowed to assume?

 

[Affinity]

But the most likely application of L'hosptial's rule will be finding some limit for graph sketching.. and they don't care which method you used

 

[redslert]

Originally posted by Affinity
But the most likely application of L'hosptial's rule will be finding some limit for graph sketching.. and they don't care which method you used

yep you don't need working for curve sketching

 

[CM_Tutor]

Originally posted by Affinity
But the most likely application of L'hosptial's rule will be finding some limit for graph sketching.. and they don't care which method you used

How would you react if someone used it to find lim (x --> 0) (sin 3x) / x ?

 

[alphatango]

It's a completely valid method to use...it's mathematically rigorous, so I don't think they'd have a problem with it. Best way would probably be to specify that you're using l'Hopital's rule, and the supervising marker (or whoever) on the scene should either be familiar with it or should be able to take it to the right person.

I guess you could regard l'Hopital's rule as a "formula" that you're not allowed to assume, but I can't really think of a case where it would depend on the result you're trying to prove -- therefore, I'd assume it's ok to use. To some extent, they *expect* that there will be 4U students who go beyond the syllabus

AT.

 

[KeypadSDM]

Screw it, I didn't use it

 

[KeypadSDM]

Originally posted by Affinity
sketch x^x for positive x...

you would have to know where it tends to as x -> 0?

Lim[x->0] x^x
= Lim[x->0] e^xLn[x]

Lim[x->0] xLn[x]
= Lim[x->0] x * Lim[x->0] Ln[x]

D'oh.

d/dx x^x = (Ln[x] + 1)x^x
d/dx x^x = 0

Ln[x] = -1
x = 1/e

1/e^1/e = 0.69...

Hence:
Lim[x->0] xLn[x] = 0

Thus
Lim[x->0] x^x = 1

Wow, that took a long time, all I had to do was plug in 0.00000001^0.00000001 = 0.999999...

Still, you don't need "The Hospital's" rule to do that