NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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