maths at uni (1 Viewer)

[mojako]

I wonder if xiao actually knows the answer ^^

 

[xiao1985]

I wonder if xiao actually knows the answer ^^

hahaha, gd pt... in fact, i was a bit intrigued by the answer my tutors giveme... because i was told in high school that if you are gievn an integral, without any other comments, u simply apply fundamental principle to it and solve it... whereas my tutors told me the integral is underfined, which now i think of it, is true...

like many of u mentioned, u cant simply evaluate the integral and get -2 as ur answer... however, if you use the limit apporach, it'd give u:

[-1 + infinity] + [-1 + infinity]...

bear in mind that infinity is not actually a number, but rather a concept, so the integral is undefined...

edit: @ jm1234567890, i mentioned how if u define integral as wut ever, is in the light of wut i was told in high school, so iwrongly thought the integral is defined and the answer is -2...

 

[mojako]

so after all these long discussions the answer is simply:
"undefined"???

Can we approximate it?

 

[jm1234567890]

so after all these long discussions the answer is simply:
"undefined"???

Can we approximate it?

It was just because xiao sensationalised it

 

[xiao1985]

so after all these long discussions the answer is simply:
"undefined"???

Can we approximate it?

well i find it intriguin how holes can just be minor to create an almost trivial soln =p

clearly a negative answer is trivial =p

 

[mojako]

so... can the integral be approximated?
with today's technology it should be able to.

btw... "eng2u adv, math 4u, chem, phys, bio, chinese bs"
too much science ^^
btw the UAI booklet says that only 6 units of science can be counted.. but I dont think there are any other science subjects besides chem, phys & bio.. (I don't think senior science cant be taken with those 3 sciences)

 

[Estel]

earth and environmental sci, and theres one more i can't remember.

 

[Euler]

you shouldn't always believe what you are told in high school. There is so much stuff left out in high school, but at the same time, it's impossible to cover everything in high school. I suppose you wouldn't ever be given a question like that at the high school level.

http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html has the conditions on applying the Fundamental Theorem of Calculus, so it's pretty clear in this case that the theorem doesn't hold because of the problem at x=0.

Taking limits, as some suggested, the integral diverges.

mojako: what is the UAI booklet? where can I get it? Can someone else confirm the limitations of 6 units of Science?

 

[velox]

u cant do more than 6u of sciences.

 

[withoutaface]

u cant do more than 6u of sciences.

Excluding maths, which is not considered a science for HSC purposes.

 

[velox]

yes of course.

 

[mojako]

I think that booklet should be distributed to (each student at) your school. hmm.. maybe not all schools.. my school as actually a private school.
It does say RRP $15.00 and it might be available from newsagency

yeah, Im glad science doesnt include maths ^^

To Estel: none of those sciences exist at my school

EDIT: it's a book, the size of Cambridge HSC 3U maths... why did I mention booklet???

Another EDIT: It's UAC book (not UAI). But I had a look at it now and it doesn't say anything about science. Just category A and B courses.
In the Rules and Procedures for 2004 HSC purple booklet, it says "To satisfy pattern of study requirements for the HSC, you may count a max of 6 preliminary units and 6 hsc units from courses in Science" without a mention of the word "UAI". But my school takes it as meaning UAI.

 

[Xayma]

btw the UAI booklet says that only 6 units of science can be counted.. but I dont think there are any other science subjects besides chem, phys & bio.. (I don't think senior science cant be taken with those 3 sciences)

For the HSC the sciences are:

Biology
Chemistry
Earth and Environmental
Physics
Senior Science.

Senior Science can be taken with the above but requires certain conditions.

Senior Science can not be selected with them for the preliminary course, however, Senior Science may be undertaken at the HSC level provided one of: Physics, Chemistry, Biology, Senior Science (Not to sure of Earth and Environmental Science) preliminary courses have been completed. Ie you can do Biology yr 11 and drop to Senior Science in yr 12.

However, when you pick it up there is no rule saying you have to drop the other sciences, indeed I know a few people at my school doing chemistry/senior science.

The UAC guide is distributed to all yr 12 students sitting the HSC in the NSW and the equivalent in the ACT.

 

[xiao1985]

Excluding maths, which is not considered a science for HSC purposes.

maths is not considered as science even in uni level, i don't think...

@majako: =p not really, i think without a face do all 3 sciences =) i know alot of people who do 3 sciences =) and i am one of them @@ and yes, u can do senior science (but i think if u do either bio/chem/phys, it forbids u do senior science) and earth and environmental... =)

the question is actual abit incomplete, the original question states how one person evaltuated usin fundamental theorem of calculus and got a negative answer, while the other student says since 1/x^2 is always above the x axis, the answer should be positive... class discussion. the answer to the q is both students are wrong, cuz tis not negative, clearly, nor is it positive... if u take the limit, u get infinity, which is not positive....

 

[mojako]

I think there is positive infinity and negative infinity...
for example, you want to examine how a particular curve behaves on the very left of the coordinate axis.. you take the lim as x approaches negative infinity...

and (I think), if you draw 1/x^2 on a computer graphing program and look on the area under the curve, it doesn't look like it will approach infinity... it might, but not t the same degree of... just say the integral of x.dx from x=0 to x=infinity.. so there is a degree of infiniteness in itself

and I'm not "majako" =p

 

[xiao1985]

@ majako, well not majako:

yes there is positive infinity and negative infinity, but the problem is that the second student said it should be a postivie NUBMER... that is clearly wrong... the area cannot be expressed as a number...

 

[jm1234567890]

@ majako, well not majako:

yes there is positive infinity and negative infinity, but the problem is that the second student said it should be a postivie NUBMER... that is clearly wrong... the area cannot be expressed as a number...

+/- infinty are only a concept, not a number in the real/complex number system

so as xiao said, they don't count as a number.

 

[psych_girl]

pure maths ---> fun
applied maths --->boring, aprt from the bit which is associated with pure maths...

Agree with you. I think pure is better than applied. haha!

 

[Li0n]

howbout engineering maths?
what level would that fall under?
and how disadvantaged would a person who did ext-1 only in year 12 be to people who did ext-2?

 

[turtle_2468]

If you're decent, it doesn't take long to catch up.