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##### Q.01 Find the discontinuities if any

**Solution:**

This a composition of two functions. Let

and

so we can write

is a polynomial which is continuous everywhere, and is continuous on . Therefore, their composition is continuous ie is continuous everywhere. There is no point of discontinuity.

##### Q.02

**Solution:**

we can write , as a composition of two functions.

Let

and

so that .

is discontinuous at those where the denominator becomes zero. Put denominators equal to zero. is point of discontinuity of is a point of discontinuity of

##### Q.03

**Solution:**

is continuous at , where the denominator and numerator are both continuous and the denominator is not zero. Since and both are continuous everywhere. Therefore will be discontinuous at all those points where the denominator .

##### Q.04

**Solution:**

where

will be discontinuous at all those points where the denominator cos

##### Q.06

**Solution:**

It is continuous everywhere because the denominator . for all .

##### Q.07

**Solution:**

will be discontinuous at all points where the denominator

are the points where the function is discontinuous.

##### Q.08

**Solution:**

will be discontinuous at all those points where the denominator