Exercise 4.1

Question 1

Find the principal value of each of the following:

(i)

Sol :

(ii)

Sol :

(iii)

Sol :

(iv)

Sol :

(v)

Sol :

(vi)

Sol :

Let

Therefore

We know that principal value of and

Therefore principle value of is

Question 2

(i)

Sol :

(ii)

Sol :

Question 3

Find the domain of each of the following functions:

(i)

Sol :

(ii)

(iii)

(iv)

Question 4

If , then find the value of

Question 5

If , find the value of