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!

Weird limit question

  1. Oct 9, 2008 #1
    1. The problem statement, all variables and given/known data

    f(x+y)= f(x) + f(y) + y*x^2 +x*y^2 Given: lim of f(x)/x where x approaches 0 is 1
    Find : 1) f(0) 2) f ' (0) 3) f ' (x)
    2. Relevant equations



    3. The attempt at a solution
    countless hours with other coursemates that lead to nothing but a looping headache.
     
  2. jcsd
  3. Oct 9, 2008 #2

    statdad

    User Avatar
    Homework Helper

    Note that

    [tex]
    f(x+y) = f(x) + f(y) + x^2 y + x y^2
    [/tex]

    means that (using [tex] x = y = 0 [/tex]

    [tex]
    f(0) = f(0) + f(0) + 0
    [/tex]

    What does this tell you about [tex] f(0) [/tex]? Also remember the definition:

    [tex]
    f'(0) = \lim_{h \to 0} \frac{f(0+h) - f(0)}{(0+h) - 0} = \lim_{h \to 0} \frac{f(h)-f(0)} h
    [/tex]

    This second point relates to one thing you are given
     
  4. Oct 9, 2008 #3
    Yep, that be true. It's the 3rd part of the question that i can't still solve. I've posted the first two parts of the question as a guide to solving the third part. So any ideas on the 3rd part? Thanks for making the second part ans more organize. My solution was a little more messy.
     
  5. Oct 10, 2008 #4
    but x+y=0, x can be -y. that is, x and y may not equal to zero?
    so f(0)=f(x)+f(-x)?
     
  6. Oct 10, 2008 #5

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    [tex] f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{(x+h)-x}[/tex]

    But given that [itex]f(x+y)=f(x)+f(y)+x^2y+xy^2[/itex] , what is [itex]f(x+h)[/itex] ?
     
  7. Oct 13, 2008 #6
    Wow, true, I didn't see it that way.Thanks a lot. LOL
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Weird limit question
  1. Weird Limit Problem (Replies: 3)

  2. Weird question (Replies: 12)

  3. A weird question in DE (Replies: 1)

Loading...