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Math Help - Linearization Help Please

  1. #1
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    Linearization Help Please

    know the linearization L(x)=f(a)+deriv (a)(x-a) is originally the tangential line to f at x=a. So, we think that for x near a, L(x)=f(x). While the change in y=f(x)-f(a)=deriv f(a).

    Change in x=deriv f(a)(x-a)
    Change in y=d=L(x)=f(x)=deriv f(a)dx
    dx=change x=(x-a)

    Even with all this i still can't get these problems..

    a.)Find the linearization of y=f(x)=sqr(1+x) at x=0

    b.) Find dy

    c.) Find dy when x=0 and dx=.2

    d.) Estimate f(.2) by the linearization

    thanks for your help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mcdaking84 View Post
    know the linearization L(x)=f(a)+deriv (a)(x-a) is originally the tangential line to f at x=a. So, we think that for x near a, L(x)=f(x). While the change in y=f(x)-f(a)=deriv f(a).

    Change in x=deriv f(a)(x-a)
    Change in y=d=L(x)=f(x)=deriv f(a)dx
    dx=change x=(x-a)

    Even with all this i still can't get these problems..

    a.)Find the linearization of y=f(x)=sqr(1+x) at x=0

    The linearisation is:

    f(x)=f(0)+f'(0)x

    where:

    f(0)=\sqrt{1}=1

    also:

    f'(x)=(1/2) (1+x)^{-1/2}

    so:

    f'(0)=1/2

    CB
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