Beispiel 21
Results 1 to 7 of 7

Thread: Beispiel 21

  1. #1
    dj_m.o.h.t.'s Avatar
    Title
    Elite
    Join Date
    Jan 2002
    Posts
    428
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Beispiel 21

    Es sei gu(u,v)=d/du * g(u,v)=u^2-v und gv(u,v)=-u+v^3. Man bestimme h(t)=d/dt * g(2t, t^2+1)!

  2. #2
    dj_m.o.h.t.'s Avatar
    Title
    Elite
    Join Date
    Jan 2002
    Posts
    428
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Meine Lösung!

    gu = u^2 - v g = u^3/3 - u*uv + c

    gv = -u+v^3 g = -uv + v^4/4 + d

    => g(u,v) = u^3/3 - u*v + v^4/4

    u = 2t, v = t^2+1

    g(t) = 8t^3/3 - 2t^3 - 2t + 1/4 * (t^8 + 4t^6 + 6t^4 + 4t^2 + 1)

    g'(t) = 8t^2 - 6t^2 - 2 + 1/4 * (8t^7 + 24t^5 + 24t^3 + 8t + 1) = 2t^7 + 6t^5 + 6t^3 + 2t^2 + 2t - 7/4

  3. #3
    bluefoxx's Avatar
    Title
    Baccalaureus
    Join Date
    Mar 2002
    Location
    Vienna
    Posts
    537
    Thanks
    0
    Thanked 0 Times in 0 Posts
    bekomm ich auch raus!

    bFXx

  4. #4

    Title
    Master
    Join Date
    Dec 2001
    Location
    Wien, 8.
    Posts
    100
    Thanks
    0
    Thanked 0 Times in 0 Posts
    ich komm auf: 2t^7+6t^5+6t^3+2t^2+2t-2

  5. #5
    lj_scampo's Avatar
    Title
    Baccalaureus
    Join Date
    Mar 2002
    Posts
    582
    Thanks
    0
    Thanked 0 Times in 0 Posts
    ich komme auch auf
    2t^7+6t^5+6t^3+2t^2+2t-2

    der fehler war bei:
    1/4 * (t^8 + 4t^6 + 6t^4 + 4t^2 + 1)' =
    1/4 * (8t^7 + 24t^5 + 24t^3 + 8t <b>+ 1</b>)
    -> der 1er faellt weg, also richtig:
    1/4 * (8t^7 + 24t^5 + 24t^3 + 8t)

  6. #6

    Title
    Principal
    Join Date
    Feb 2002
    Location
    Reintal
    Posts
    56
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Bsp 21

    Robby, wie kommst du denn bei g'(x) am Schluss auf 7/4??

    Danke. Lg.

  7. #7

    Title
    Principal
    Join Date
    Mar 2002
    Location
    Wien
    Posts
    89
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Meine Lösung!

    Original geschrieben von robby
    gu = u^2 - v g = u^3/3 - u*uv + c

    gv = -u+v^3 g = -uv + v^4/4 + d

    => g(u,v) = u^3/3 - u*v + v^4/4

    Äh, Glaub ich steh ein bisschen auf der Leitung, aber wie kommt mann auf "-u*uv", bzw auf das "-uv" ???

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •