Taylor series Write out the first three terms of the Taylor series for the following functions centered at the given point a. Then write the series using summation notation.

f(x) = e3x, a = 0

Solution 27RE

Step 1:

In this problem we have to find the first three terms of the Taylor polynomial for function with the given center point a=0.

Taylor series is given by

In our case,

So, what we need to calculate derivatives, evaluate them at the given point.

Step 2:

Then

Then

Then