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  1. W

    Self-Taught Calculus

    well I'm 17 and started to learn it when I was 16 :) I'm a self-taught too. If you work hard why not man? everything is possible.
  2. W

    Can't get this

    yeah I know it, I said I did it that way. But the problem is that nothing is told about it. Anyway thnaks, I think the question wasn't complete in this case
  3. W

    Can't get this

    that's because of this. suppose that a=x+y and b=xy then \sqrt (a + 2\sqrt b) = \sqrt x+ \sqrt y Ivy, I don't get what you mean. How do you know if the numbers x and y are rational then the only solution is x=y=0.5? and how do you know there is an infinite number of solutions if they...
  4. W

    Can't get this

    How does he implies that? I got there before but I supposed that x and y are not irrational
  5. W

    Can't get this

    can't get this!!! Hi there, I have a question that I cannot solve. Here it is. \frac{1}{\sqrt(4-2\sqrt3)}=x+y\sqrt3 then what is x^2+y^2? All I did was finding what left hand side stood for. It equals \frac{\sqrt3 + 1}{2} Any help?
  6. W

    Finding an antiderivative using substitution rule

    replace 2x by u and you have secu 's derivative under the integral sign
  7. W

    Need help deriving a formula

    Try to draw the velocity-time graph. The area under the curve will give you the displacement.
  8. W

    Values of a and b

    oh yes thank you everybody. I must be getting dumber by each second to miss this...
  9. W

    Values of a and b

    Yes but isn't there an algeabric way to calculate those values?
  10. W

    Values of a and b

    Well thanks but I just introduced myself to the integral calculus so I do not understand anything from what you say. edit: btw graphing doesn't count it is too easy using the graph
  11. W

    Values of a and b

    \int_a^b (x-x^2)dx What values of a and b make this integral's value maximum? I have tried to do it but cannot get it. I know that the maximum value of x-x^2 is 0,25. but I'm stuck from there. I try to write the integral in the form of a riemann sum but (b-a)s cancel each other.what am I to...
  12. W

    Your Favorite Quote

    I do not feign hypotheses - "Isaac Newton" If I have seen further than others, it is by standing upon the shoulders of giants. - "Isaac Newton" I can calculate the motion of heavenly bodies, but not the madness of people. - "Isaac Newton" and of course some darth sidious quotes. So...
  13. W

    Pi(x) function in number theory solved

    My method is new (is the first method to calculate pi(x) involving an integral and not a sum) so i think is worth publishing,the problem perhaps is that i am not famous and can not compete with these snobish teachers of important universities publishing nonsenses and useless things , sorry i...
  14. W

    Newton's Lemma 28

    I never thought that way but it is not needed. It's like the lines that are in theradar screens. I looked at your diagram, but the process is, I think, like building a circle by using a line segment and revolving it around a point. The two are similar. We use the point's place on the line to...
  15. W

    Newton's Lemma 28

    As far as I am concerned, we use the point's place on the line that revolves around the pole. I have shown the proportionality thus. You said that the line can intersect the spiral at most 3 times. I don't understand this because I think it is at most 1. That is because the spiral is made up...
  16. W

    Newton's Lemma 28

    We are considering the full extension of course. The point is proportional to the area that's what is important for us. Whether it is inside the circle or not doesn't matter... And "the" line is the one that moves with uniform speed...
  17. W

    Newton's Lemma 28

    As to the appliance of the law of areas to the square, I don't think it is possible. the law says that in an oval, ellipse precisely, the areas swept in equal times are equal. But what happens the line skips a corner while moving with uniform motion in the square? I don't think it would work
  18. W

    Newton's Lemma 28

    Hehe anytime... As I have said D.T Whiteside published a counter-example for this in Mathematical Papers of Isaac Newton, if I'm not mistaken. But it's a pain in the neck to find those books. I don't see anything wrong with newton's proof now, but as soon as I see Leibniz's or Whiteside's...
  19. W

    Newton's Lemma 28

    That is not a correct point of view. I have used Kepler's area law to show that the place of the point is proportional to the area. Kepler's Law is not valid for squares.The proof was flowed because I hadn't seen that in order to have an infinite number of gyrations we should revolve the line...
  20. W

    Newton's Lemma 28

    Oh right you are! I'm sorry. But I will help you now and I think I got everything right. If you have read Newton's original text he says that if we can express the area of the oval by a finite equation we can find the place of the point at a given time. You were right about the gyration part...
  21. W

    Newton's Lemma 28

    The hand moves around uniformly, but the moving point speeds up and slows down in the course of each hour, in proportion to the square of the distance from the pole to the oval at any given moment. Each hour it returns to its initial speed of an hour before. If you were to watch the lighted...
  22. W

    The hardest logical puzzle according to George Boolos

    My first question would surely be are you a god? :) If I am lucky I learn two things :)
  23. W

    Newton's Lemma 28

    Well, I have just started reading Principia but as soon as I have seen this post I couldn't restrain myself from checking out. I think I have found a way to explain this. Let C be the area of the oval. This is a fixed number. Let T be the time it takes for the straight line to come to the...
  24. W

    Calc problem (area of parametric curves)

    try to write t in terms of x and then replace t with what you have found in the other equation...
  25. W

    Strange trig problem

    Have you tried to draw the problem to help you understand better? What progress have you made?
  26. W

    Opinions on this ?

    yes, what's wrong with it?
  27. W

    X in terms of a

    Do you mean something like this? English is not my native tongue so I have a little difficulty with mathematical terms. this is what I have now x^2+x-\sqrt (z+a) -z^2=0
  28. W

    Line tangent to an elipse given one point

    you can use limit as well. that would be using the derivative but you would derive the function yourself...
  29. W

    Area of trapezium

    If that was an answer to my post, there exists such a formula and it is called Heron's Formula. It is used to find the area of a triangle only by using the sides. What I did is clear and correct. Integral provided just another way to find the area. If you have a look at my attachment in my...
  30. W

    X in terms of a

    Ummm, yes that's what I have but it seems I have written it wrong. I should have 8 roots x in terms of a in this case but I can only think of newton's method to find those. That is not a very good idea actually...
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