Defenition of Limit

Discussion in 'Math' started by Tails, Feb 13, 2007.

  1. Tails

    Thread Starter New Member

    Feb 13, 2007
    5
    0
    I'm stuck on a calc problem, and its lim of tanx.

    Here is the whole thing:

    By using the defenition f'(a)=lim (f(a+h)-f(a))/h and taking smaller


    values of h, estimate the value of f'(pi/4).

    When i plug in the limit definition, the numbers really seem to jump around, or is that what i use to find the values? Anyway, can somebody help me with this problem? its due tomorrow. Thanks.








    NOTE: due to the lack of symbols, "pi" is used in place of the greek letter
     
  2. Papabravo

    Expert

    Feb 24, 2006
    9,912
    1,724
    Then you are doing something wrong. The limit you are taking is an approximation to the derivative of tan(x), not the value of the function itself. The answers that you get should be closer and closer to 2, which is the value of the derivative of tan(x) at pi/4. Is your calculator set for degrees or radians? To compute tan(pi/4) you need to make sure that it is set to radians.
    Code ( (Unknown Language)):
    1.  
    2. ((tan(pi/4 + .01) - tan(pi/4)))/.01 = 2.02...
    3. ((tan(pi/4 + .001) - tan(pi/4)))/.001 = 2.002...
    4.  
    d(tan(x))/dx = 1 / cos^2(x) = 1 /(.707)^2 = 1 / 0.5 = 2

    you can also make h negative and approach the value from the other side.
     
  3. Tails

    Thread Starter New Member

    Feb 13, 2007
    5
    0
    i was doing it wrong... i was looking at "h" as being "a" (pi/4) and i realized "h" shouldve been 0 in the table, and i looked, and the answers do approach 2 when the x value in my calc is 0, which is h.
     
  4. Papabravo

    Expert

    Feb 24, 2006
    9,912
    1,724
    Glad I could be helpful.

    Remember also that this approximation for the derivative requires that the function tan(x) be continuous in a neighborhood of pi/4 and that the derivative is defined in the same neighborhood. Plus or minus pi/2 violates this condition and thus you cannot use the approximation to evaluate the derivatve of tan(x) at plus or minus pi/2
     
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