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To derive a linearized form of following equations

  1. Mar 20, 2010 #1
    hello

    suppose a eqn is given as y=x/(ax+b). which we can linearize as: (1/y)=a+b/x and therefore Y=A+BX where A=a, B=b and X=1/x .Another example is y=ax^b this can be written as ln y=ln ax^b or ln y=ln a+bln x therefore Y=A+bX where Y=ln y,A=ln a and X=ln x thus it is linearized now. I tried to do the following ones in the same way but failed.Could anyone help me by linearizing this way please,
    the problems are: 1) y=1/{(x+a)(x+b)}^1/2
    2)y=x^2/(ax+1)(bx+2)

    linearizing that is we have to write in y=ax+b form
    thanks
     
  2. jcsd
  3. Mar 20, 2010 #2

    Filip Larsen

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    Linearization usually means something a bit different than the procedure you seem to indicate here. What it usually means is to find a and b for the line y = ax+b such that the line is a first order approximation for the function y = f(x) at point x = x0, i.e. the line passes through f(x0) with a slope of f'(x0). See for instance http://en.wikipedia.org/wiki/Linearization.
     
  4. Mar 20, 2010 #3
    ok then can you tell me how to convert the equations in y=ax+b form?
     
  5. Mar 21, 2010 #4

    Filip Larsen

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    Gold Member

    So you want to find two transformations X(x) and Y(y) such that Y(y) = aX(x)+b whenever y = f(x)?

    For the two first functions you found X and Y as the same transformation (i.e. 1/x and log(x), respectively). Is this required to be so by the problem description or is it allowed for them to be different transformations? If they can be different then maybe solving y = f(x) for x (i.e. finding the inverse of f(x)) may provide you with something.
     
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