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 Definition of Derivative

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Use the limit definition of derivative to determine the derivative of the following function:

    f(x) = { sqrt(x^2+1) if x<=0
    0 if x>0

    2. Relevant equations

    I'm not sure as to why the function is not continuous at x=0, and so it's not differentiable at that point.

    3. The attempt at a solution

    The left-hand limit and right-hand limit give me 0. And if I plot a graph, the graph hits 0 as it moves from one function to the other.
  2. jcsd
  3. Nov 16, 2009 #2


    User Avatar
    Science Advisor

    The left hand limit is "1", not "0"! I would think that would be obvious. What is f(-0.001)?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook