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Exponential function

  1. Aug 1, 2009 #1
    1. The problem statement, all variables and given/known data

    This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

    2. Relevant equations


    3. The attempt at a solution
    then how about the e^(-1)=?
    Besides what is the function of sin x and cos x in continued function (such in e^x)?
  2. jcsd
  3. Aug 1, 2009 #2
    I'm not really for sure what your question even is. What problem are you trying to solve? Are you asking for the power series for sine and cosine?
    \sin x &= x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \\
    \cos x &= 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots

    Or are you asking for the following identities?
    \sin x &= \frac{e^{ix}-e^{-ix}}{2i} \\
    \cos x &= \frac{e^{ix} + e^{-ix}}{2}
  4. Aug 1, 2009 #3


    Staff: Mentor

    e-1 = 1 + (-1) + (-1)2/2! + (-1)3/3! + ... + (-1)n/n! + ...
  5. Aug 1, 2009 #4


    Staff: Mentor

    Also, you have posted what appears to be the same question twice, which is frowned upon in this and most other forums.
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