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Math Help - Differentials - Check my work

  1. #1
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    Differentials - Check my work

    Not sure I am working these problems correctly. I watched some youtube videos and think I figured it out but would like you to verify my work.

    Find the differential of the function. Calculate dy for the given valuse of x and dx.

    1) y=sqrt(1+x^2), x=0 dx=0.01

    f'(x)=1/2(x^2+1)^(-1/2) (2x) = x/sqrt(x^2+1)
    dy=f'(x)dx
    dy=x/sqrt(x^2+1)dx
    dy=0/sqrt(0^2+1)(0.01)=0

    2) y=x^3-6x^2+5x-7, x=-2 dx=0.1

    f'(x)=1/4 x^4 - 2x^3 + 5/2 x^2 - 7x

    dy = f'(x)dx
    dy = (1/4(-2)^2-2(-2)^3 +5/2(-2)^2-7(-2))(0.1)
    dy = 4.4

    3) cos^2(pit), t=1/3 dt=0.05

    f'(t) = -2pi cos(pit)sin(pit)
    dy=f'(t)dt
    dy = -2pi cos(pi/3)sin(pi/3)(0.05)
    dy = -2pi (1/2)(sqrt(3)/2)(0.05)
    dy = 1/20(sqrt(3)/4)pi
    dy = pi sqrt(3)/80 = 0.068

    Thank you for looking,
    Rod
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  2. #2
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    Re: Differentials - Check my work

    I noticed i did #2 wrong...

    f'(x) = 3x^2 - 12x + 5
    dy = (3(-2)^2 -12(-2) + 5)(.1)
    dy = 4.1
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  3. #3
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    Re: Differentials - Check my work

    Did you try wolfram alpha? Doesn't it do stuff like this?
    Last edited by SuccessfulSeductress; November 22nd 2012 at 09:10 AM.
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  4. #4
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    Re: Differentials - Check my work

    Thanks for the tip.

    You can enter this type of problem in wolfram?

    I am hopeing someone will take the time to let me know if i got the concept correct.
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  5. #5
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    Re: Differentials - Check my work

    On #3, you lost a factor of 2 and a minus sign.

    - Hollywood
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  6. #6
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    Re: Differentials - Check my work

    Thanks Hollywood!,

    Other than the error you noted, what i showed is the correct process for this type of problem?
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  7. #7
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    Re: Differentials - Check my work

    Yes, your method is correct, and your answers to #1 and #2 are also correct.

    - Hollywood
    Thanks from MarkFL
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