Calculus I

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  • #13247

    Ezra Halleck
    Participant

    4.1: Find the linearization of the given function centered at and use it to estimate ,
    ; find the error using a calculator.
    First find the derivative and evaluate at a then determine dx and use to find dy. The error is to find the (absolute value of the) difference between the f(b) and f(a)+dy.

    #16813

    Danielle Telemaque
    Participant

    L(x) = f’ (a)(x-a) + f(a)

    f(x) = (1)/(x^2-9) = (x^2-9)^(-1/2)

    f(x)’ = (-1/2)(x^2-9)^(-3/2) * 2x

    f(a) = (1)/(5^2-9)^(1/2) = (1/4)

    f(a)’ = (-1/2)* (25-9)^(-3/2) * (10)
    = -5(16)^(-3/2)
    = (-5/64)

    L(5.01) = (1/4)- (5/64)*(5.01-5)
    = (1/4)- (5/64) *(0.01)
    = 0.24921875

    Approx = 0.24921815

    Error = 0.24921875-0.24921815= 0.0000006

    %Error= 0.0002075 %

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