Are we are allow to use L'Hospital's Rule for lim question

[Saturn WY15]

So basically can we use L'Hospital's Rule for lim question (lim x>0 sinx/x) etc

[TheBloop]

No… that's just 1. You should just know that.

[TheBloop]

Also, L'hopital's rule isn't in the syllabus so maybe avoid it.

[Timske]

lol

[iSplicer]

Also, L'hopital's rule isn't in the syllabus so maybe avoid it.

+1.

[RealiseNothing]

I'd avoid it. I use it in school exams but for externals I'm not going to.

[Riproot]

I'd avoid it. I use it in school exams but for externals I'm not going to.

if you can't use an alternate method in school what makes you think you'll be able to for HSC?

[cutemouse]

So basically can we use L'Hospital's Rule for lim question (lim x>0 sinx/x) etc

Probably not. Otherwise it'd be in the syllabus.

[RealiseNothing]

if you can't use an alternate method in school what makes you think you'll be able to for HSC?

I am allowed to use alternate methods in school.

[D94]

So basically can we use L'Hospital's Rule for lim question (lim x>0 sinx/x) etc

In high school, it's sort of an identity that the limit of sin(x)/x = 1, and they say that due to small angle approximations. Since they treat it as an identity, you just need to manipulate similar questions to get it into the form of sin(x)/x or likewise.

But you can't use L'H for the HSC.

[mirakon]

if you can't use an alternate method in school what makes you think you'll be able to for HSC?

I think you are technically allowed to but its stupid because

a) As you and D94 have pointed out, there is an easy method in the syllabus which can be used
b) If your marker does not have the mathematical knowledge to understand the alternate methods you use, its likely they will assume you're talking out of your ass and give you minimal marks. In other words, its risky and tbh if you have the ability to comprehend and utilise out of syllabus mathematics, you should have the ability to solve those questions with the methods in the syllabus anyway

[Saturn WY15]

I think you are technically allowed to but its stupid because

a) As you and D94 have pointed out, there is an easy method in the syllabus which can be used
b) If your marker does not have the mathematical knowledge to understand the alternate methods you use, its likely they will assume you're talking out of your ass and give you minimal marks. In other words, its risky and tbh if you have the ability to comprehend and utilise out of syllabus mathematics, you should have the ability to solve those questions with the methods in the syllabus anyway

Yeah i know but i just find it so much easier using the L'Hospital rule. Oh well ;0

[Nick_K]

In first year maths at sydney uni our lecturer told us not to use L'Hopital's rule for sinx/x because it is used when establishing d/dx(sinx), creating a circular argument. There is another way to set up the trig functions that bypasses the issue but it just might be worth noting.

[cutemouse]

Another way is the taylor series expansion.

ie. sin x / x = (x-x^3/3!+x^5/5!- ....) / x = 1 - (x^2/3!-x^4/5!+...)

It is clear that if you set x->0 then sin x / x -> 1.

[SpiralFlex]

You shouldn't see any questions that require L'hospital's rule in 3U. Though Saturn's tutor said it can be used in 4U.

[Carrotsticks]

No, don't use it.

The HSC is there to test HOW WELL you can apply what you're meant to know, not just how much you know out-of-syllabus things (though of course that helps sometimes).

[asianese]

No - the questions involving these are easy enough!!

[Carrotsticks]

(is that a challenge?)

[Shadowdude]

Another way is the taylor series expansion.

ie. sin x / x = (x-x^3/3!+x^5/5!- ....) / x = 1 - (x^2/3!-x^4/5!+...)

It is clear that if you set x->0 then sin x / x -> 1.

Yes because Taylor Series is part of the HSC...

[asianese]

Haha carrot, no it is not, but by the trend of the questions that related to these identities (sinx/x, x/sinx, tanx/x, x/tanx) are quite straightforward.

[Nooblet94]

(is that a challenge?)

Oh yes please!

[asianese]

Haha trust nooblet94

[FBJ]

I thought any theorem/technique should be allowed as long as you say what it is and use it correctly.

[Nooblet94]

I thought any theorem/technique should be allowed as long as you say what it is and use it correctly.

Pretty sure that if you want to use something outside the syllabus you have to derive it.

[Johnstan]

Yes because Taylor Series is part of the HSC...

umm its actually been in a few question 8's in 4unit over the years...
me and my cousin were doing this yesterday lol:P