# Search results

1. ### I forgot the clever way of doing these integrals...

\int \frac{\sin^2 x - 4\sin x \cos x + 3\cos^2 x}{\sin x +\cos x}dx
2. ### MATH2701 Abstract Algebra/Fundamental Analysis

Don't need to show me how to do the entire question if it's way too long. Suggestions are plenty :) f(x)=\int_x^{x+2\pi}\frac{\sin t}{t}dt \text{Prove that }f(x)=O(x^{-2})\text{ as }x\to \infty My starting point was just saying f(x) < integrand being 1/t instead of sint/t, but working...
3. ### MATH2621 Higher Complex Analysis

\text{For }z=x+iy \text{ find the image of }x+y=4\text{ under the mapping }w=z^{-1}
4. ### MATH2901 Higher Theory of Statistics

f,g\text{ are increasing functions and }X,Y\text{ are i.i.d. r.v.s} \text{RTP: }(f(X) - f(Y))(g(X) - g(Y)) \ge 0
5. ### What is MATH2701 like?

Basically as the title suggests. I don't really know who to ask (Shadowdude maybe?) so I'm just leaving this here. Does anyone have any insight on how difficult this course is and any tips to doing well in it?
6. ### MATH2601 Higher Linear Algebra

\text{Define an operation}*\text{over }\mathbb{Z}_n\text{ where }x*y=xy \mod n\\ \text{Proven earlier: This operation is binary, commutative and associative} \text{Let }p\in \mathbb{Z}\text{ be prime. Show that }\mathbb{U}_p=\mathbb{Z}_p - \{ 0\}\text{ is a group under the operation }*\text{...
7. ### Six people topped the state this year

http://www.boardofstudies.nsw.edu.au/ebos/static/FSTIC_2016_12.html
8. ### Prerequisites

Can someone please tell me what MATH2221 and MATH2621 are prerequisites for? I want to figure out what to do first
9. ### Has anyone here done AMus?

Just curious. Because idk if it's something I should consider after 8th grade.
10. ### Quick terminology question

What's the difference between calling it a geometric "series" as opposed to a geometric "progression"? Or is there none
11. ### HSC 2017 MX2 Integration Marathon (archive)

Post integrals here to help/test the Extension 2 students of 2017 Here is a decent question to begin \int_0^1 x^2\sqrt{3-x^2}dx Note that there are still unanswered questions in the 2016 marathon that you may like to consider.
12. ### 2010 HSC Question

4d A group of 12 people is to be divided into discussion groups. (i) In how many ways can the discussion groups be formed if there are 8 people in one group, and 4 people in another? (ii) In how many ways can the discussion groups be formed if there are 3 groups containing 4 people...
13. ### Transformers question

Can someone please carefully explain why the answer is A and not B? It appears to defy Is/Ip=np/ns Thanks in advance.
14. ### Motion Analysis

\text{The acceleration }a\, \textit{ms}^{-2}\text{ of a particle moving in a straight line is given by }a=3\left(1-x^2\right)\text{, where }x\text{ metres is the displacement of the particle to the right of the origin.}\\ \text{Initially, the particle is at the origin moving at a velocity of...
15. ### Energy Conversions calculations question

Have no idea how to do this one. Apparently the answer is B.
16. ### Complex numbers lost in the typos

I don't really mind if the question is left incomplete, but can someone please suggest some correction to part (ii) to make it easier for me to understand please. I can't decipher it myself
17. ### Fertiliser Calculations question

Can someone please do this question and check my working/answer? The answer wasn't given. I ended up with A. Q: A student wants to determine the sulfate content of a fertilizer. Following a typical procedure, they obtain the results shown below. Mass of fertilizer used = 2.34g Mass of...
18. ### MATH1081 Discrete Maths

Don't mind me...just setting up some threads for more of my stupidity this upcoming semester. UNSW course outline: https://www.maths.unsw.edu.au/sites/default/files/math1081-s2_2016.pdf
19. ### First Year Mathematics B (Integration, Series, Discrete Maths & Modelling)

Don't mind me...just setting up some threads for more of my stupidity this upcoming semester. 1231/1241 Outline: https://www.maths.unsw.edu.au/sites/default/files/math1231_math1241_s2_2016.pdf 1251 Outline: https://www.maths.unsw.edu.au/sites/default/files/math1251_s1_2016.pdf
20. ### Polynomials question

I only need the second part of part (iii). Everything else I could get out but I get something wrong for the proof. P(x)=x^4+Ax^3+Bx^2+Ax+1\\ x=\alpha\text{ is a zero.} \text{(i) Given that }(2+B)^2\neq 4A^2\text{, show that }\alpha \neq 0, \pm 1 \text{(ii) Show that }x=\frac{1}{\alpha}\text{...