Search results

  1. D

    What tutor to pick

    Yes, I still take students, but only a few.
  2. D

    Maths Help

    3. \frac {dy}{dx} = e^{2y}\\ \\ \therefore \frac {dy}{e^{2y}} = dx \\ \\ \therefore \int dx = \int e^{-2y} dy \\ \\ \therefore x = -\frac {1}{2}e^{-2y} + C
  3. D

    Maths Help

    2. \frac {dy}{dx} = 1 - \frac {y}{3} = \frac {3 - y}{3}\\ \\ \therefore \frac {dy}{3-y} = \frac {dx}{3}\\ \\ \therefore \int \cdots dy = \int \cdots dx \\ \\ \therefore -ln |3-y| = \frac {x}{3} + C \\ \\ x = 2 \implies y = 4 \implies -ln|3 - 4| = \frac {2}{3} + C \implies C = -\frac {2}{3} \\...
  4. D

    Binomial Distribution Assignment Help

    Question too bloody long!
  5. D

    How do I do this complete mindblank

    You can use the "Terry Lee" method to find the square root of -60-32i. Here's how: \sqrt{-32i - 60} = 2\sqrt{-8i -15}\\ \\ \sqrt{-8i - 15} = \sqrt{1 - 8i -16} = \sqrt{1^2 + 2\times 1 \times ({-4i}) +(-4i)^2} \\ \\ \\ $Remember: $ (a + b)^2 = a^2 + 2 \times a \times b + b^2 = (a + b)^2 \\ \\...
  6. D

    confused with this q

    A^4 + 4B^4 = A^4 + 4B^4 + 4A^2B^2 - 4A^2B^2 \\ \\ = (A^2 + 2B^2)^2 - (2ab)^2 = (A^2 + 2B^2 +2AB)\times(A^2 + 2B^2 - 2AB)
  7. D

    how to improve in maths

    I don't think you can get an easy answer here. If you can afford it, get a good tutor to check you out or a friend who is good in maths to help you.
  8. D

    Is reverse chain rule just integral of product of function and it's derivative?

    Maybe I'll show you how to do RCR later.
  9. D

    forgot how to integrate this

    \int ^1 _0 \frac {\sqrt x}{1 + x} dx = \int ^1 _0 \frac {\sqrt x}{1+(\sqrt x)^2} \times 2\sqrt x d\sqrt x\\ \\ =2\int^1 _0 (1 - \frac {1}{1 + (\sqrt x)^2} )d \sqrt x \\ \\ =2 \left[\sqrt x - tan^{-1} \sqrt x \right ]^1 _0 \\ \\ = 2[(1 - \frac {\pi}{4} ) -(0 - 0)] = 2 - \frac {\pi}{2} \\ \\...
  10. D

    Is reverse chain rule just integral of product of function and it's derivative?

    Integrands which are derivatives(or constant multiples thereof) of composite functions are the ones usually handled by "integration by substitution". They often refer to reverse chain rule - but I've seldom seen how this reversal is achieved. Using my method, I can do the reversal of the chain...
  11. D

    is motion in a straight line

    Motion, in general, does not need to be in a straight line. In your Adv & Ext 1 Maths, you are usually dealing with motion in a straight line, because this is the easiest to deal with. Motion in a straight line is often referred to as "rectilinear motion".
  12. D

    9b, a bit confused (calculus)

    \frac {dy}{dx} = -3\frac {d}{dx}(x^4-2x^2-1)^{-1} = -3\frac{d(x^4-2x^2-1)^{-1}}{d(x^4-2x^2-1)} \times \frac {d(x^4-2x^2-1)}{dx}\\ \\ = -3\times {-1}(x^4-2x^2-1)^{-2} \times (4x^3-4x) \\ \\ = \frac{3\times 4x(x-1)(x+1)}{(x^4-x^2-1)^2}\\ \\ = 0 $ at x $=0, -1,1\\ \\ y(-1) = \frac {-3}{1-2-1} =...
  13. D

    Integration question

    Again, if not required to use the substitution: \int ^0 _{-3} \frac {x}{\sqrt {1-x} }dx = -\int ^0 _{-3}\frac {1-x - 1}{\sqrt {1-x} }dx\\ \\ = \int ^0 _{-3} (1-x)^{0.5} d(1-x)-\int ^0 _{-3}(1-x)^{-0.5}d(1-x)\\ \\ = \left[ \frac{2}{3}(1-x)^{1.5} -2(1-x)^{0.5} \right]^0 _{-3} \\ \\ =-(\frac...
  14. D

    is this 3u

    Avoiding formal substitution: \int ^1 _0 x\sqrt{1-x^2} dx = -\frac {1}{2}\int ^1 _0 (1-x^2)^{0.5} d(1-x^2) \\ \\ =-\frac{1}{2} \left[\frac {(1-x^2)^{1.5}}{1.5} \right]^1 _0 = -\frac {1}{2}\left [ (\frac{2}{3} \times(1-1)^{1.5}) -(\frac {2}{3}(1-0)^{1.5})\right ]\\ \\ = -\frac{1}{2} \times...
  15. D

    confused and rusty on this any help appreciated

    a) \int y\sqrt{y+1}]dy = \int (y+1 - 1)\sqrt {y+1} d(y+1) \\ \\ = \int ((y+1)^{\frac {3}{2}} - (y+1)^\frac{1}{2}) d(y+1) = \frac{2}{5}(y+1)^\frac{5}{2} - \frac{2}{3}(y+1)^\frac {3}{2} + C c) \int \frac {x}{\sqrt{2x-1}} dx = \frac {1}{2}\times \frac {1}{2}\int \frac {(2x-1 + 1)}{\sqrt{2x-1}}...
  16. D

    Is it worth keeping maths extension 1?

    Try to find out why you were not doing better? What areas were you having difficulties in your MX1; can you do better with more effort? Put in extra effort and learn from any "mistakes" you may have made in your 1st test. Now see how you go in your next test and see how you go, before deciding...
  17. D

    How do I improve in Maths?

    You need to provide more details of what happened. Which new topics were you experiencing problems with. When you got lower marks, why were you getting lower marks? etc etc. Without more background info, we can only guess what or where your difficulty lies.
  18. D

    Geometric Proving

    Above from an old Signpost Year 8 Book. Say we are given a parallelogram ABCD. e start with the definition of the parallelogram, in this case only that it is a quadrilateral with opposite sides, viz AB & DC and AD & BC being parallel. That's all we are given. How do you prove that: i) AB = DC...
  19. D

    Geometric Proving

Top