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Math Help - Differentials?

  1. #1
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    Differentials?

    With the information given compare delta y and dy.

    1. y=(x)^3 x=1 delta x= 0.1

    dy= f'(x)(dx)

    dy= 3(1)(0.1)

    dy=.3

    delta y= f(x+delta x)- f(x) I am having trouble finding delta y

    delta y= (1+.1)-(1) ? Is this what I would do


    My second question is similar

    2.y= x^4+1 x=-1 and delta x=.01

    dy=(-4)(-1)(.01)
    dy=.04

    But I am having trouble finding delta y
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  2. #2
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    Re: Differentials?

    y = x^3

    x = 1 , \Delta x = 0.1

    \frac{\Delta y}{\Delta x} = \frac{y(1.1) - y(1)}{1.1 - 1} = \frac{1.1^3 - 1}{1.1 - 1} = \frac{0.331}{0.1}

    therefore ...

    \Delta y = 0.331


    y = x^3

    \frac{dy}{dx} = 3x^2

    dy = 3x^2 \cdot dx

    dy = 3(1^2) \cdot (0.1) = 0.3


    see the difference between \Delta y and dy ?
    Attached Thumbnails Attached Thumbnails Differentials?-deltay.jpg  
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  3. #3
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    Re: Differentials?

    Your response was very helpful indeed.
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