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Linear approximation given accuracy points

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Round the answers to two decimal places.)
    tan(x) ≈ x

    2. Relevant equations

    derivative of tan(x) = sec^2(x)

    3. The attempt at a solution

    f(0)= tan(0)=0
    fprime(0)= sec^2(0)= 1
    L(x)=f(a)+fprime(a)(x-a)
    L(x)=0+1(x-0)
    L(x)=x

    not sure how to continue from here
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 15, 2012 #2

    SammyS

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    I don't think you need to derive the result.

    Graph y=tan(x) and y=x for -1 ≤ x ≤ 1 or some similar interval near zero.

    Make a table of x and tan(x) for some values starting at x=0, and continuing until you have a difference of 0.1.
     
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