Chapter 9 Continuity Ex 9.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10(i)

Solution 10(i)

Question 10(ii)

Solution 10(ii)

Question 10(iii)

Solution 10(iii)

Question 10(iv)

Solution 10(iv)

Question 10(v)

Solution 10(v)

Question 10(vi)

Solution 10(vi)

Question 10(vii)

Solution 10(vii)

Question 10(viii)

 Discuss the continuity of the following functions at the indicated points:

Solution 10(viii)

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Also sketch the graph of this function.Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Determine the values of a, b, c for which the function

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36(i)

Solution 36(i)

Question 36(ii)

Solution 36(ii)

Question 36(iii)

Solution 36(iii)

Question 36(iv)

Solution 36(iv)

Question 36(v)

Solution 36(v)

Question 36(vi)

Solution 36(vi)

Question 36(vii)

Solution 36(vii)

Question 36(viii)

Solution 36(viii)

Question 36(ix)

In each of the following, find the value of the constant k so that the given function is continuous at the indicated point:

Solution 36(ix)

Question 37

Solution 37

Question 38

Solution 38

Question 39(i)

Solution 39(i)

Question 39(ii)

Solution 39(ii)

Question 40

Solution 40

Question 41

Solution 41

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

is continuous at x = 3.Solution 46

Question 42

For what of  is the function  continuous at x = 0? What about continuity at x = ±1?Solution 42

Given: 

At x = 0, we have

∴ LHL ≠ RHL

So, f(x) is discontinuous at x = 0.

Thus, there is no value of  for which f(x) is continuous at x = 0.

At x = 1, we have

∴ LHL = RHL

So, f(x) is continuous at x = 1.

At x = -1, we have

∴ LHL = RHL

So, f(x) is continuous at x = -1.

Chapter 9 Continuity Ex 9.2

Question 1

Solution 1

Question 2

Solution 2

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 3(v)

Solution 3(v)

Question 3(vi)

Solution 3(vi)

Question 3(vii)

Solution 3(vii)

Question 3(viii)

Solution 3(viii)

Question 3(ix)

Solution 3(ix)

Question 3(x)

Solution 3(x)

Question 3(xi)

Solution 3(xi)

Question 3(xii)

Solution 3(xii)

Question 3(xiii)

Solution 3(xiii)

Question 4(i)

Solution 4(i)

Question 4(ii)

Solution 4(ii)

Question 4(iii)

Solution 4(iii)

Question 4(iv)

Solution 4(iv)

Question 4(v)

Solution 4(v)

Question 4(vi)

Solution 4(vi)

Question 4(vii)

Solution 4(vii)

Question 4(viii)

Solution 4(viii)

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Given the function

Find the points of discontinuity of the functions f(f(x)).Solution 18

Question 19

Find all point of discontinuity of the function 

Solution 19