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ERJAEE, G. (20)

Lecture 28

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

28This

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MATH 2B - Lecture 28 - Taylor Series & Maclaurin Series

● We have learned for certain type of functions, we can use a geometric type

power series as representations.

● Now we will consider a more general case, to represent a continuous F(x) by

using a general power series

Certain type “Geometric” Power Series Convergence

General Function Power Series Convergence

F(x)

Suppose we can represent some functions F(x) as power series

● F(x) =

● Now the question is how can we determine the coefficient for each term

First, let’s write the first 5 terms of the series

●

● If we plug in a for x, we notice that all the terms except the first term become zero

○

● Now, we take the derivative of F(x)

○

● Now we plug in a for x again, such that

○

● We can further take the second derivative:

○

● Plug in a for x, we obtain

● The third derivative gives us

○

● Let x = a,

○

So, in summary we have:

●

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