Limit thingy (1 Viewer)

[shinji]

heya, just a question

in 2u course, do we learn how to do:

Lim sin x
x-> 0 x

?

coz that was in my trial and im not sure if i twas part of the 3u or 2u course . . . lol

 

[aethr]

I remember seeing questions like that in the 2U MIF Book so I'd assume it would be in the syllabus.

The answer should be 1 if im not mistaken.

 

[ditto]

yeah it looks like small angles problems but where does the '0' in the denominator come in?

 

[Sober]

heya, just a question

in 2u course, do we learn how to do:

Lim sin x
x-> 0 x

?

coz that was in my trial and im not sure if i twas part of the 3u or 2u course . . . lol

If you find that you cannot solve a problem like that with a limit then most of the time you can just sub 0.0001 into the calculator as x then key in the expression. Most of the time it will give you an answer considerably close to the correct one such as 0.9997. The only times this does not work is when there is a radical solution and the answer wants you to be exact.

The same goes for lim x -> infinty, you can often sub in 9999999999 for x.

 

[rama_v]

This is in the camrbdige 2 unit book, for small angles sin @ = approximately @ . But it does look like a 3 unit question.

 

[darkliight]

l'Hopital's makes these easy.

If you've got lim x->c f(x)/g(x), but subbing in c gives an indeterminate form like 0/0 or inf/inf, then lim x->c f(x)/g(x) = lim x->c f'(x)/g'(x), provided the new limit exists (note you can use l'Hopital's again, provided you get another indeterminate form).

In this case, lim x->0 sin(x)/x gives the indeterminate form 0/0, so we can use l'Hopital's, giving us lim x->0 cos(x)/1 = 1.

 

[SoulSearcher]

I don't ever remember learning this in 2 unit maths last year, but it might have been an oversight made by either me or my teacher last year.

 

[shinji]

lol. i knw how to solve it, but i was wonderin whether or not it was in the 2u course.

and thx rama,

yeah .. i usually assosciate it with 3u so i was shocked to see a similar question to this in my 2u trial

 

[robo-andie]

There are questions in the 2unit paper which are designed to seperate the 3u students from 2u. This question may be one of them.

 

[shinji]

There are questions in the 2unit paper which are designed to seperate the 3u students from 2u. This question may be one of them.

..but the 2u students should still be able to do those questions yeah?

i mean ... if its not in the 2u syllabus they can't be tested on it..

 

[word.]

There are questions in the 2unit paper which are designed to seperate the 3u students from 2u. This question may be one of them.

there are questions which are designed to separate the better students to the best students who usually just happen to be 3 unit students... but in any case there will never be a question in the 2 unit paper which is out of its syllabus i.e. any extension-only topics, if that's what you were implying...

as for the topic,
the limiting behaviour of trigonometric functions as they approach 0 is a part of the 2 unit course.