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!

In the set?

  1. Jan 25, 2012 #1
    If G=the set of all continuous complex-valued functions on the interval [0,1] and [itex]f,g \in G[/itex] then is [tex]\displaystyle f(x) \int^1_0 g(t) \; dt - g(x) \int^1_0 f(t)\;dt[/tex] in G?

    If H=the set of all differentiable complex-valued functions on the interval [0,1] and [itex]f,g \in H[/itex] then is [tex]fg' - gf'[/tex] in H?
     
  2. jcsd
  3. Jan 25, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]\int_0^1 f(x) dx[/itex] and [itex]\int_0^1 g(x)dx[/itex] are numbers so, knowing that f and g are continuous, what can you say about Af+ Bg for constants B and G?

    The derivative of f'g+ fg' is f''g+ 2f'g'+ fg''. Knowing that f and g are differentiable what can you say about f'' and g''?
     
  4. Jan 25, 2012 #3
    Got it. They're both still in the sets.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: In the set?
Loading...