1. Not finding help here? Sign up for a free 30min 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!

Calculus problem, explaining the step

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data
    dy/dx(x+dx) - dy/dx(x-dx)
    => d^2y/dx^2 when dx->0

    can someone explain this step to me please?



    2. Relevant equations

    The dx in the brackets should be sigma x

    3. The attempt at a solution
    I know that dx -> means it tends to zero

    i think i might have missed something out that might make a difference to this step;
    it may be necessary to divide through the first line by dx (sigma x) to complete the step? Im stumped, i dont see how this works at all.
     
    Last edited: Oct 30, 2007
  2. jcsd
  3. Oct 30, 2007 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Write h for 'dx' in 'brackets'. Then you are saying lim h->0 y'(x+h)-y'(x-h)=y''(x). Not true. It's ok if you divide the left side by 2*h. It's just a difference quotient representation of a derivative.
     
  4. Oct 31, 2007 #3
    Yes, my notes show that i divide the left hand side by h, but i still dont understand how this makes the left hand side into a 2nd order derivative?
     
  5. Oct 31, 2007 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The derivative of f(x) can be defined by the limit of f(x+h)-f(x-h)/(2h) (yes, 2h). Put f=y and you get a definition of derivative y'. Now put f=y'.
     
    Last edited: Oct 31, 2007
  6. Oct 31, 2007 #5

    say h = 0.1, and i put f=y', i would get (1.1 - 0.9)/0.2 = 1
    how does this mean that it equals f''?
     
  7. Oct 31, 2007 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You said "I know that dx -> means it tends to zero". You have to take the limit as h->0 to get the true derivative.
     
  8. Oct 31, 2007 #7

    I see, im sorry if im missing an obvious point here, but i still cant see how as h tends to zero it makes the formula become a second derivative.

    I chose 0.1 because it was a relatively low number to see if i could understand the workings of the equivalence we are studying. So as h gets smaller and smaller i still get the answer of 1, and when h is zero i get:

    (f'x - f'x)/0

    which equals zero - OOOOOOOHHHHH - and that is what it equals as a second derivative! I didnt realise that, but i see how that works now, i think. Thankyou Dick, i got there in the end i guess.
     
  9. Oct 31, 2007 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Don't put h=0! The result is undefined! Take the limit as h->0. Look back at the definition of a 'derivative'.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Calculus problem, explaining the step
Loading...