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

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: