Results 1 to 4 of 4

Math Help - derivative

  1. #1
    Banned
    Joined
    Jul 2009
    Posts
    107

    derivative

    We know that the position vector in physics is defined as:

    r(t) = x(t)i +y(t)j +z(t)k ,where i =(1,0,0) ,j=(0,1,0) and k=(0,0,1).

    Prove that :

    \frac{dr(t)}{dt} = \frac{dx(t)}{dt}i + \frac{dy(t)}{dt}j + \frac{dz(t)}{dt}k
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    What have you tried? Where are you getting stuck?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Jul 2009
    Posts
    107
    Quote Originally Posted by Defunkt View Post
    What have you tried? Where are you getting stuck?
    From the very beggining i don't know what the limit :

    lim_{\Delta t\to 0}\frac{r(t+\Delta t)-r(t)}{\Delta t} is equal to
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by alexandros View Post
    From the very beggining i don't know what the limit :

    lim_{\Delta t\to 0}\frac{r(t+\Delta t)-r(t)}{\Delta t} is equal to
    Just replace r(t+\Delta t) and r(t) by their expressions in terms of the basis vectors and collect components:

    \lim_{\Delta t\to 0}\frac{r(t+\Delta t)-r(t)}{\Delta t} = \lim_{\Delta t\to 0}\left(\frac{x(t+\Delta t)-x(t)}{\Delta t}\textbf{i} \right. + \frac{y(t+\Delta t)-y(t)}{\Delta t}\textbf{j} + \left. \frac{z(t+\Delta t)-z(t)}{\Delta t}\textbf{k} \right)

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 03:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 12:40 PM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 07:33 AM
  4. Derivative of arctan in a partial derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 12th 2010, 02:52 PM
  5. Replies: 2
    Last Post: November 6th 2009, 03:51 PM

Search Tags


/mathhelpforum @mathhelpforum