[Mike Graham]

Originally Posted by slap_j

William of the hospital...

So, the hospital's rule.

You are translating proper names. You are not allowed to do that.

[Mike Graham]

Originally Posted by jbm222

In this case,

lim x-->0 x / sin(3x) = "0/0" <--- meets condition for L'Hopt.

Applying L'Hop

= lim x-->0 1 / 3*cos(3x) = 1 / 3*cos(0) = 1/3*1 = 1/3

You are making a mistake here.

x/sin(3x)=

(d/d(x))(x) / (d/d(x))(sin(3x))=

1 / (3*cos(3x)) (note: you could jump to the answer at this point)

(1/3) * (1/cos(3x))

(1/3) * sec(3x)

(1/3) * 1

Originally Posted by jbm222

As far as Maru's method.... that might be easier for you, but that's one more formula to remember

I would be inclined to agree. I made it through a year and a half of calculus without learning the u/sin(u) identity (and have yet to use it since I learned it), but don't think I would have made it through two weeks without knowing L'Hopital's rule.

[jbm222]

Where's the mistake?

I probably should have been more clear in my notation, but I was just showing that in this case after you take the derivates you can just subsitute 0 for x.

lim x-->0 cos(3*x) = cos(3*0) = cos(0) = 1.

I don't understand why you felt the need to factor out 1/3 and change 1/cos to sec before making the x=0 substitution.

[Mike Graham]

I think perhaps I misunderstood when you said "1 / 3*cos(3x)." By order of operations, this would be .3333*cos(3x). Looking back I realize you might have meant "1/(3cos(3x))."

[slap_j]

Originally Posted by Mike Graham

You are translating proper names. You are not allowed to do that.

You're not the boss of me.

[jbm222]

You're right. Thanks. i'll have to remember that. I dunno why I wrote it that way since Maple, Matlab, and TI calculators would all interpret it the way you did.

[smhatahy]

soo does L'Hospital sound like it looks or does it sound like Lopital

my calc teacher pronounced it Lopital

[jbm222]

The first syllable is 'low'. I don't know about the other two. I've heard the 'pi' like pizza and pickle, and the 'tal' like tall and talent.

[smhatahy]

my teacher grew up in the philipines and speaks french fluently.. and she said it was lopital..

[Jay Tea]

I always pronounced it LOW pee tahl