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Math Help - Use differentials (or equivalently, a linear approximation) to approximate...

  1. #1
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    Use differentials (or equivalently, a linear approximation) to approximate...

    Use differentials (or equivalently, a linear approximation) to approximate as follows: Let and find the equation of the tangent line to at a "nice" point near . Then use this to approximate .

    Approximation =
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  2. #2
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    The linearization (linear approximation) of f(x) about x = a is given by f(a) + f'(a)(x-a). Let a = \pi/3 be the "nice" point and x = 55\pi/180 (I'm using radians to make things easier).
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  3. #3
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    Quote Originally Posted by nehme007 View Post
    The linearization (linear approximation) of f(x) about x = a is given by f(a) + f'(a)(x-a). Let a = \pi/3 be the "nice" point and x = 55\pi/180 (I'm using radians to make things easier).
    thanks but do you mind showing maybe the next couple of steps because I have no clue what to do with the given information
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  4. #4
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    f(x) = sin(x) implies that f'(x) = cos(x). Plug the values of x and a that I suggested into f(a) + f'(a)(x-a).
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