# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 9

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## State Whether the Statements Are True or False in Each of the Exercises 42 to 46

**Question 42:**

For continuity, at , each of and is equal to .

**Answer: True**

**Question 43:**

is a continuous function.

**Answer: True**

**Question 44:**

A continuous function can have some points where limit does not exist.

**Answer: False**

**Question 45:**

is a differentiable function for every value of *.*

**Answer: False**

**Question 46:**

is differentiable everywhere.

**Answer: True**

## 5.3 EXERCISE

### Short Answer (S.A)

**Question 1:**

Examine the continuity of the function

**Answer:**

We have,

And

And

So, is continuous at

### Find Which of the Functions in Exercises 2 to 10 is Continuous or Discontinuous at the Indicated Points

**Question 2:**

**Answer:**

And

Since,

So, is discontinuous at .

**Question 3:**

**Answer:**

At

And

Since,

Hence, is not continuous at