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Linear approximation to approximate a value

  1. Oct 16, 2012 #1
    1. The problem statement, all variables and given/known data
    f(x) = sqrt(1 - x)
    a = 0

    Approximate sqrt(0.9).

    2. Relevant equations
    L(x) = f'(a)(x - a) + f(a)


    3. The attempt at a solution
    I understand that linear approximation is finding the equation of a line of a point tangent to a function. But now this question is asking me to approximate the value of sqrt(0.9), which I assume means without the use of a calculator. The given function is sqrt(1 - x) and a = 0. So f(0) = 1 and f'(0) = -1/2. Therefore the equation of the line tangent at (0,1) of this function is -x/2 + 1. How does this have anything to do with finding the value of sqrt(0.9)?
     
  2. jcsd
  3. Oct 16, 2012 #2

    Dick

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    The tangent line is close to the curve sqrt(1-x) if x is close to zero. So you can approximate value of the curve by the value of the tangent line. What value of x would you use?
     
  4. Oct 16, 2012 #3
    Oh, 1 - x = 0.9 so 0.1

    Okay, I got it now
     
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