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Method of differentials

  1. Aug 30, 2006 #1
    I am completly lost on these differentials! Can anyone help me make sense of them? Especially this question in particular:


    (Sorry, I don't know how to make that small little circle thing that denotes degree)

    I'm supposed to use the method of differentials to estimate it to 4 decimal places.

  2. jcsd
  3. Aug 30, 2006 #2


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    Show what you've tried. Do you know how to use this method?

    By the way, I'd never heard of the "method of differentials" before, and I had to do a google search to figure out what it is. It seems to just be synonomous with "linear approximation", or, if you want a higher order approximation, "taylor series approximation", by which names I think the method is much more well known. Just another reason to always show your work if you want help.
  4. Aug 30, 2006 #3


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    45 degrees is [itex]\frac{\pi}{4}[/itex] radians. 1 degree is [itex]\frac{\pi}{180}[/itex] radians. It's better to use radians because that way the derivative is easier: if x is measured in radians then the derivative of y= cos(x) is y'= -sin(x) and so the differential is dy= -sin(x)dx. y+ dy= cos(x)- sin(x)dx.
    To find [itex]cos(\frac{pi}{4}+ \frac{\pi}{180}[/itex], let [itex]x= \frac{\pi}{4}[/itex] so that [itex]y= cos(\frac{\pi}{4})= \frac{\sqrt{2}}{2}[/itex], [itex]-sin(x)= -sin(\frac{\pi}{4})= -\frac{\sqrt{2}}{2}[/itex] and [itex]dx= \frac{\pi}{180}[/itex].
  5. Aug 30, 2006 #4
    Oh Thanks!

    Thanks you guys, My text books are a little backwards it seems. Where one asks me to use method of differentials the other teaches linear aproximation, that was so confusing and now I see why. Thanks A bunch!
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