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\int \frac{\sin^2 x - 4\sin x \cos x + 3\cos^2 x}{\sin x +\cos x}dx

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...

\text{For }z=x+iy \text{ find the image of }x+y=4\text{ under the mapping }w=z^{-1}

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

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?

\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{...

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

Can someone please tell me what MATH2221 and MATH2621 are prerequisites for? I want to figure out what to do first

Just curious. Because idk if it's something I should consider after 8th grade.

What's the difference between calling it a geometric "series" as opposed to a geometric "progression"? Or is there none

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.

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...

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

\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...

Have no idea how to do this one. Apparently the answer is B.

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

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...

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

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

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{...