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Recent content by fan96

  1. fan96

    Hard Proofs Question

    I think there's a possibility that there's some algebraic trick you can do (independent of the previous parts) to find C once you know that it actually exists. Part v) specifically states that the limit exists (with a DO NOT PROVE attached). That would be unnecessary and possibly misleading...
  2. fan96

    Inequalities question help

    Hint: Make the substitutions a = e^\alpha, b = e^\beta, c = e^\gamma.
  3. fan96

    Need help with a parametric equation question thanks

    If you plot this using software the graph you get is not the same as the original parametric equation. (You only get the upper half of the graph.) This theorem requires f to be invertible wherever x is defined. The input \theta + \arctan(1/4) varies over an interval of length 2\pi , where...
  4. fan96

    Need help with a parametric equation question thanks

    Observe that x + y = 9 \cos \theta 5x - 4y = -9 \sin \theta so \left(x+y\right)^2+\left(5x-4y\right)^2=81.
  5. fan96

    discrete mathematics

    Are we talking about the UNSW course? If so then I didn't really like it. Out of the seven math courses I've done so far I'd rank this near the bottom, tied with or just above MATH2221 Differential Equations. It suffers from the same problem as the other first year math courses where you don't...
  6. fan96

    Polynomial question help!!

    That isn't quite what I said - I said if a,b,c were constants then the expression is a polynomial. What sort of polynomial it is, we can't tell without further information. For the polynomial to be quadratic we require a -2 \ne 0 , which cannot be the case since the polynomial is the zero...
  7. fan96

    Polynomial question help!!

    The question introduced (a-2)x^2+(1-3b)x+(5-2c) as simply a polynomial (which it is, if we assume a, b, c are constants). It never claimed this polynomial was a quadratic and in fact it is not, because quadratic equations must be expressible in the form \alpha x^2 + \beta x + \gamma where...
  8. fan96

    Linear Algebra

    "Linear Algebra" is a massive field of study, so a comprehensive formula sheet would be at least the size of a textbook. You would have to explicitly give the course outline for your linear algebra course - and at that point you could just take notes on lectures and make your own. Also, your...
  9. fan96

    Simple 2U Trig Help

    -\pi and \pi are typically both used to describe the angle of the negative x-axis (i.e. they're both really the same angle). 0 \le x \le \pi are the 1st and 2nd quadrants. -\pi \le x \le 0 are the 3rd and 4th quadrants. So -\pi \le x \le \pi describes all four quadrants.
  10. fan96

    help for proofs

    Where did you get this question? You probably wouldn't be able to get this result from just e^n \ge {(n+1)^n}/{n!} as \frac{(n+1)^n}{n!} \stackrel{?}{\ge}1+n^2 is not actually true, even taking n \ge 0. You'd have to at least start a bit further back. I doubt this is the intended answer...
  11. fan96

    Mistakes with trivial arithmetic

    Usually I'd expect a mistake like this to only incur a 1/2 mark penalty. If it was really really minor (e.g. you wrote the wrong units) then you might even get away for free.
  12. fan96

    Hard enrichment question from the Cambridge textbook!

    In more concrete words, you are asked to show n = \cos^{-1} \frac 35, given the conditions a \cos \alpha = 1, a \cos (n+\alpha) = 5, a \cos (2n+\alpha) = 5. So, try to solve for n . You have three equations with as many variables, so intuitively this should be solvable. Bonus points -...
  13. fan96

    Mechanics question

    Actually, the simplest way is to just get the answer from the back of the textbook, ask someone else who knows how to do it, or to search it up online. And this is what we would do if we only cared about the number we get at the end. So what is the point of even learning calculus and...
  14. fan96

    Binomial Help

    \binom{n}{2} \left(\frac{9}{10}\right)^{n-2} < \binom{n}{3}\left(\frac{9}{10}\right)^{n-3} \frac 1{10} Divide by (9/10)^{n-3}: \binom{n}{2} \left(\frac{9}{10}\right) < \binom{n}{3} \frac 1{10} Now use \binom{n}{k} = \frac{n!}{(n-k)! \, k!} so \frac{n!}{(n-2)! \, 2!}...
  15. fan96

    "Describe the motion..." mechanics question

    Your reasoning is correct. Another way to look at it is the following: If O is any point that is not \pi/2 , then the particle will start off with a positive velocity, which means its displacement will increase. But when its displacement increases, its velocity ( v = \cos^2x ) gets smaller...