University of Florida/Egm4313/s12.team8.dupre/R2.7

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R2.7

Problem Statement[edit]

Develop the Maclaurin series (Taylor Series at t=0) for

a) (7-1)

b) (7-2)

c) (7-3)

Solution[edit]

For a Taylor series at any point t, the general form is as follows (to make it more clear, I have changed the usual t in (t-a) to a capital T):

Part a solution[edit]

Using (7-4) as applied to (7-1) at time t=0 gives us the Maclaurin series for (7-1):



Simplifying this result, we obtain our final solution:


Part b solution[edit]

Using (7-4) as applied to (7-2) at time t=0 gives us the Maclaurin series for (7-2):



Simplifying this result, we obtain our final solution:



Part c solution[edit]

Using (7-5) as applied to (7-3) at time t=0 gives us the Maclaurin series for (7-3):



Simplifying this result, we obtain our final solution: