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Thread: Find the limit, as h -> 0, of [ f(h) - f(-h) ] / h

  1. #1

    Find the limit, as h -> 0, of [ f(h) - f(-h) ] / h

    Hello,

    I'm struggling with this calculation:

    lim (f(h)-f(-h))/h
    h->0

    These were given in the assignment:
    f(0) = -3
    f'(0) = 5

    I've tried basically everything and am at a loss. Thank you if you can help me solve the exercise.
    Paula.

  2. #2
    Elite Member
    Join Date
    Jun 2007
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    17,180
    Quote Originally Posted by paula12345 View Post
    Hello,

    I'm struggling with this calculation:

    lim (f(h)-f(-h))/h
    h->0

    These were given in the assignment:
    f(0) = -3
    f'(0) = 5

    I've tried basically everything and am at a loss. Thank you if you can help me solve the exercise.
    Paula.
    Rewrite:

    lim (f(h)-f(-h))/h
    h->0

    = lim (f(0+h)-f(0-h))/h
    h->0

    Now use the definition f'(x) to continue....
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Senior Member
    Join Date
    Dec 2014
    Posts
    1,408
    Quote Originally Posted by Subhotosh Khan View Post
    Rewrite:

    lim (f(h)-f(-h))/h
    h->0

    = lim (f(0+h)-f(0-h))/h
    h->0

    Now use the definition f'(x) to continue....
    Am I missing something or do we need to know what f(x) is?
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

  4. #4
    Elite Member
    Join Date
    Jan 2012
    Posts
    4,217
    No, you only need the derivative of f at x= 0.
    Last edited by HallsofIvy; 11-25-2016 at 01:23 PM.

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