Using a graphing utility to graph the functiton and visually estimate the limits:

Question

f(x) = xcosx

1. lim        f(x)

            x--->0

1. lim        f(x)

            x--->pi/3

Answer 1

Step 1:

The function is .

Graph of the function :

 

 

Step 2: 

(a)

The limit of  tends to 0, as x approaches 0.

Thus,  

 

Step 3:

(b)

The limit of  tends to 0.52, as x approaches .

Thus,

 

Solution:

(a) .

(b) .