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!

Limit help

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data

    (f(x+h) - f(x)) / h

    f(x) = 2/x
    x = -4

    As h approaches 0

    2. Relevant equations
    N/A


    3. The attempt at a solution
    (2/(-4 + h) + 1/2) / h


    Don't know where to go from there though, not sure how to simplify.
     
  2. jcsd
  3. Sep 2, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    So you want to compute this :

    ##lim_{h→0} \frac{f(x+h) - f(x)}{h}## when ##f(x) = \frac{2}{x}## and ##x=-4##.

    My advice is leave the x=-4 until the very end in these types of problems and just work with this :

    ##lim_{h→0} \frac{\frac{2}{x+h} - \frac{2}{x}}{h}##

    Find a common denominator for the numerator and simplify it, then apply this rule :

    ##\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}##.

    You'll be able to find the limit easily afterwards.
     
  4. Sep 2, 2013 #3
    In response to what Zondrina said...

    when simplifying ##lim_{h→0} \frac{\frac{2}{x+h} - \frac{2}{x}}{h}##,
    I use a method called the butterfly method...

    Just cross multiply the denominator of the left fraction with the numerator of the right fraction and the denominator of the right fraction with the numerator with the left fraction and finally multiply the denominators of both fractions to get this...

    ##\frac{\frac{2x-2(x+h)}{(x+h)x}}{h}##

    Then use the rule suggested by Zondrina with the h: ##\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}##
     
    Last edited: Sep 2, 2013
  5. Sep 2, 2013 #4
    Got it, thanks a lot guys!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Limit help
  1. Limit help (Replies: 5)

  2. Help with Limits (Replies: 5)

  3. Help with limits (Replies: 4)

  4. Help with a limit (Replies: 3)

  5. Help with a limit. (Replies: 1)

Loading...