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: Given a piecewise, prove that it is continous and differentiable

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    For f(x)= { sin(x)/x if x≠0 , 1 if x=0. (a) Show that f is continous and differentiable for all x. (b) Show the derivative f'(x) is continous.


    2. Relevant equations



    3. The attempt at a solution
    I know that if f is differentiable it is continous, so I need to focus on x=0 to show that the function is differentiable. And now I'm stuck lol
     
  2. jcsd
  3. Dec 4, 2011 #2

    hunt_mat

    User Avatar
    Homework Helper

    Write down the definition of the derivative at x=0.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook