The function is

(a)

The maclaurin series of is , .

Consider .

Replace with .

.

Observe the series it is undefined at .

In function is defined at .

Therefore, the function is not equal to its maclaurin series.

(b)

Graph the function

Observe the graph:

As tends to , the function value approaches to .

.

(a) The function is not equal to its maclaurin series.

(b) Graph of the function

As tends to , the function value approaches to .

.