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Math Help - Estimating Using Differentials

  1. #1
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    Estimating Using Differentials

    I'm trying to understand this concept but the teacher kind of made it unclear.

    The problem is

    a. Sqrt(108)
    b. Sqrt(1002)

    For a. what the teacher did was:

    a = 100 x = 8
    F(x) = sqrt(x) F'(x) = 1/2sqrt(x)

    Am I supposed to use the Linearlization formula to estimate this? Also why is a = 100 and x = 8?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Afterme View Post
    I'm trying to understand this concept but the teacher kind of made it unclear.

    The problem is

    a. Sqrt(108)
    b. Sqrt(1002)

    For a. what the teacher did was:

    a = 100 x = 8
    F(x) = sqrt(x) F'(x) = 1/2sqrt(x)

    Am I supposed to use the Linearlization formula to estimate this? Also why is a = 100 and x = 8?
    if your formula is f(x) \approx f(a) + f'(a)(x - a), then you use x = 108 and a = 100 (where f(x) = \sqrt{x})

    that's using linear approximation. very close (indeed, equivalent) to using differentials, it should be acceptable

    (by what you wrote, i am sure your professor said a = 100 and dx = 8)
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