(a)

The infinite series for the inverse tangent function is .

Consider the first five terms of .

.

(b)

Find the approximate value of .

.

(c)

Graph:

Graph the function and the third partial sum :

Graph the function and the fourth partial sum :

Graph the function and the fourth partial sum :

.

(d)

As increases, the graphs of the partial sums more closely resemble the graph of on the interval .

Outside of the interval , the end behavior of the polynomial approximations causes the graphs of the partial sums to diverge from the graph of .

(a)  .

(b) .

(c)

Graph of the function and the third partial sum is

Graph of the function and the fourth partial sum  is \ \

Graph of the function and the fourth partial sum  is

.

(d)

As increases, the graphs of the partial sums more closely resemble the graph of on the interval .

Outside of the interval , the end behavior of the polynomial approximations causes the graphs of the partial sums to diverge from the graph of .