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Some help need please

  1. May 7, 2005 #1
    We did this new mathematics thing in class today which I did not understand, it came under the topic of differentiation.

    Firstly we were given the equation

    f(x)=E^x

    Then find the value of F(x) for x=0
    F(0)=E^0
    F(0)=1
    therefore (0,1)

    Then it said find the equation of the tangent at x=0

    Which I worked out to be Y(tangent)=X+1 [I will call this equation t(X)]

    Then it said draw up a table ranging from -.2 to .2 with increments of 0.05 for the equation

    [f(x)-t(x)/f(x)]*100

    Now my question is what the hell are we finding here??

    Thanks in advance for any help.
     
  2. jcsd
  3. May 7, 2005 #2

    dextercioby

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    Who's t(x)...?

    Daniel.
     
  4. May 7, 2005 #3

    HallsofIvy

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    First of all, it is "e", not "E". Mathematically, small and capital letters may represent very different things.

    Second: "Then it said draw up a table ranging from -.2 to .2 with increments of 0.05 for the equation

    [f(x)-t(x)/f(x)]*100

    Now my question is what the hell are we finding here??"

    My question is "what the hell are you talking about??":smile:
    You haven't told us what t(x) is! I suspect that you meant t(x) to be x+ 1, the tangent line. In that case, you are finding the percentage error in using the tangent line to approximate ex around x=0.
     
  5. May 7, 2005 #4
    Thanks for that, just what I was after. I mentioned what t(x) was but I agree it was not clear enough.

    Hmm, HallsofIvy do you know any alternatives to this method?
     
  6. May 7, 2005 #5
    Differentials can approximate functions at a specific point.

    [tex]\Delta y \approx f'(x) \Delta x[/tex]

    The change in a function at near point [itex]f(x)[/itex] is approximately the numerical derivative at x multiplied by the small change of x.
     
  7. May 8, 2005 #6

    arildno

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    Here is what I guess you were supposed to be doing:
    1) Let [tex]f(x)=e^{x}[/tex]
    2) The best linear approximation to f(x) at x=0 is given by [tex]t(x)=f(0)+f'(0)(x-0)=x+1[/tex]
    this is also called the tangent line to f at x=0
    3) You are now to find the PERCENTWISE RELATIVE ERROR E(x) between f(x) and t(x) at the interval given:
    [tex]E(x)=(\frac{f(x)-t(x)}{f(x)})*100[/tex]
     
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