Consider the function ln(x + 1) and do the following.
a. Find the MacLaurin series expansion for n = 4
b. Plot ln(x + 1) and its series expansion using your graphing calculator with a window of [0, 3] X [0, 1] with Yscl = .1.
c. We use series to approximate values of functions. Therefore it is important that we know for which values of x the series will provide good approximations of the given function. Based on the graph can we use the MacLaurin series expansion to approximate ln(x + 1) for any value of x or is there a limit to the values of x? If there is a limit then what interval provides the x - values for which the MacLaurin series expansion will provide a good estimate of the value of ln(x + 1)? Explain.
d. What effect does increasing the number of terms in the series expansion have on the way it approximates the given function? Why?