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!

Homework Help: Limit question

  1. Jul 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Use this limit for the following problems: lim as h approaches 0 of [f(x+h)-f(x)]/h.

    f(x)=[tex]\sqrt{x}[/tex], x=7

    2. Relevant equations

    3. The attempt at a solution

    lim as h approaches 0 of [f(x+h)-f(x)]/h

    = lim as h approaches 0 of ([tex]\sqrt{7+h}[/tex]-[tex]\sqrt{7}[/tex])/h

    I'm having trouble simplifying the numerator, is there any way to get rid of the square roots in the numerator? Thank you.
  2. jcsd
  3. Jul 25, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Rationalize the numerator

    [tex] \frac{ (\sqrt{7+h} - \sqrt{7})( \sqrt{7+h} + \sqrt{7})}{h( \sqrt{7+h} + \sqrt{7}}[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook