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  1. T

    ODE project please help

    Thanks for looking it over. Your right that is a much easier method. But in the second part of the question it states "show that when \gamma \geq 1 then the source must have an infinite lifetime. The way I took this is that if it is to have an infinite life then the \lim _{t...
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    Arithmetic question

    If M(x,y) is in terms of both x and y then I would say no, because you only have one equation and two unknowns
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    ODE project please help

    Im sorry, I posted this in the wrong section, feel free to move it to the homework section. Hey guys, Ive really been needing some help with this one. Im doing an assignment for Ordinary Differential Equations and I was hoping someone could help me out by looking over my work. Ive been...
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    Help with an integration by parts problem

    A substitution should work, try u=pi(t)^.5
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    A calculus problem

    Pay attention to the direction they are traveling in, and where their start points are. The woman does not travel due south from the mans initial point she is east of him. If you draw this out you should see that the distance between them after time t is not just a vertical line.
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    Finding the antiderivative

    Oh I guess you edited it since I last saw it. The first integral is correct now. For the second just try a substitution.
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    Unusual Integral?

    I'm pretty sure there is no integral for this that is defined by elementary functions. If you look around the forum I think Ive read at least one or two with the same question.
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    Taylor series Mostly conceptual

    Oh ok I see. I was looking at the wrong answer, I think. Thanks though
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    Taylor series Mostly conceptual

    I was just curious why when doing a taylor series like xe^(-x^3) we must first find the series of e^x then basically work it from there, why cant we instead do it directly by taking the derivatives of xe^(-x^3). But doing it that way doesnt give a working taylor series why is this so?
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    Need Help with Improper Integrals

    The best explanation that I could find on the way to treat infinity is here http://www.math.vanderbilt.edu/~schectex/commerrs/ just control f and type in infinity, it is in the other common calculus errors section. If you have studied limits with l`hospitals rules then you should understand...
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    Need Help with Improper Integrals

    Well nearly correct you would have the limit approach -infinity because e^x is multiplied by the -1/2. But just a word of warning when speaking math one shouldnt refer to infinity as a number, it is more of an expression meaning that the term gets larger all the time. So on work try not to...
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    Need Help with Improper Integrals

    Remeber what happens when you have a number raised to a negative power ex. x^(-2)=1/(x^2) so the limit as x approaches infinity ultimately brings this term to zero. This is basically what happens to the -t^2 in your problem. its like [-1/2+1/2(1/(e^t^2))]
  13. T

    Imaginary numbers

    So it could be either pi/2, or 2pi/3 but considering that 8 is a positive number then the angle must be pi/2 right?
  14. T

    Imaginary numbers

    w=8i I need to put this in polar form but how can i do this since this would be w=8(cos(theta)+isin(theta)) I cant find the angles because tan(theta)=8/0 which of course is undefined. Is there something that I am doing wrong?
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    Quick question on tables and integration

    so if a is any real number i can do this, but if any nonconstant variable is there than I need to find another way? Sorry it has been a while since Ive done this.
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    Quick question on tables and integration

    ok so here is the problem \int\frac{dx}{\sqrt(x^2-4x)} the table integral I am supposed to use is this \int\frac{du}{\sqrt{u^2-a^2}}=ln(u+\sqrt{u^2-a^2}+C Is it proper to make my u=x^2 and a=2x^(1/2) I am asking because the solution guide tells me to complete the square, and then...
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    Integration by parts?

    I havent actually done it but if you are right up to that point then it appears that all you have to do is make a simple u substitution to solve the integral. \int \frac{x}{x^2 +1} {}dx
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    Integration by parts?

    Take it to be 1* arctan(...) then your dv will be 1.
  19. T

    Integration by parts and simplifying

    oh yeah thats right...I always forget that its really easy to check these types of problems...thanks for all the help
  20. T

    Integration by parts and simplifying

    oh yeah thats right...ok so if i integrate that then its simply -(1/x) correct?
  21. T

    Integration by parts and simplifying

    Hi, I have been working on this problem for the longest time and have just run in circles with it. Im thinking the answer is obvious but for some reason Im missing it. I need to find \int \frac{ln(x)}{x^2} dx I know that I need to use integration by parts and have tried a number of things...
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    General series question

    I just started studying series and I was curious if there is any way to recognize the types of series i.e.(harmonic, geometric, telescoping etc.) without writing out the first five or so parts of the series. What strategies do some of you use when identifying the types of series?
  23. T

    Improper integral

    Right, sorry I was thinking of something else when i did that substitution. I think I understand this now, thanks for all the input.
  24. T

    Improper integral

    Sorry I've been sitting here trying to understand this but I'm still confused. How does this substitution help because if we make x=2secu then we have \int \frac{dx}{(2sec(x))\sqrt{(2sec(x))^2-4}} but how is this more manageable than the previous equation.
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    Improper integral

    ok but why would i pick that as the substitution, what strategy did you use to choose that as a substitution
  26. T

    Improper integral

    \int \frac{dx}{x \sqrt{x^2-4}} there are bounds to this problem but it is irrelevent since my problem is with the integration and not finding the limits. this integral resembles that of arcsec(x) but im not sure how to deal with the -4. is there any way to solve this with partial...
  27. T

    Advice on volume of solids NOT of revolution?

    say you are integrating a cube, then the area of a typical cross section would be l*w. for a cone it is pi*r^2 etc..it really depends on what kind of solids you are trying to find the volume of. But a cross section is just an infinitely thin slice out of the solid.
  28. T

    Integration of arctan(u)

    so then you are saying that by using integration by parts i should be able to prove this?
  29. T

    Integration of arctan(u)

    hi im having trouble integrating arctan(u). i have no idea where to even start. i know the derivative of arctan is \frac{1}{x^2+1} so i would assume that the integral would be the opposite? but i am supposed to prove that (arctan(u))=u(arctan(u))-\frac{1}{2}ln(1+u^2)+C i am completely...
  30. T

    Cant simplify?

    ok i understand what is going on now, but why do we chose to multiply the numerator and denominator by 2, and why do we chose 2 rather than any other number.
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