1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding maximum percentage error using differentials?

  1. Mar 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Here is the question along with the solution:

    Can anyone explain why the terms I circled in red are different? For the first term there is a negative sign but then the second term does not? Why did it disappear?
  2. jcsd
  3. Mar 5, 2013 #2
    You sum the absolute values to get an approximate upper limit. You don't know in which direction the error might be, therefore you need to do this. If dM/dx = -5 and dM/dy = 5, then you would say the error would be 5-5 = 0 (with |deltax| and |deltay| set accordingly) whereas it may have been 10. Remember you only know the absolute values of the errors, therefore you need to estimate your error using the maximum possible error on the set [x-deltax, x+deltax] X [y-deltay, y+deltay].
    You could also say that this follows from the triangle inequality, but only approximately since second derivatives may play a role at a sufficient distance.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted