# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 5

Get unlimited access to the best preparation resource for CBSE/Class-12 Business-Studies: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 127K) ↧

**Question 17:**

Verify Rolle’s Theorem for the function, in

**Answer:**

Given . Note that:

(i) The function is continuous in as is a sine function, which is always continuous.

(ii) , exists in , hence is derivable in

(iii) and

Conditions of Rolle’s Theorem are satisfied. Hence there exists at least one such that . Thus

**Question 18:**

Verify mean value theorem for the function in.

**Answer:**

(i) Function is continuous in as product of polynomial functions is a polynomial, which is continuous.

(ii) exists in and hence derivable in .

Thus conditions of mean value theorem are satisfied. Hence, there exists at least one such that

Hence (since other value is not permissible).

## Long Answer (L.A.)

**Question 19:**

If find the value of so that becomes continuous at .

**Answer:**

Given,

Therefore,

Thus

If we define , then will become continuous at . Hence for to be continuous at

**Question 20:**

Show that function given by is discontinuous at

**Answer:**

The left hand limit ofat is given by

Similarly,

Thus therefore, does not exist. Hence is discontinuous at .