Solutions of chapter 29. Limits | RD Sharma - Mathematics - Class 11

RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 29. Limits

Subject: Maths - Class 11^th

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Chapter Exercises

Exercise 29.1

Exercise 29.2

Exercise 29.3

Exercise 29.4

Exercise 29.5

Exercise 29.6

Exercise 29.7

Exercise 29.8

Exercise 29.9

Exercise 29.10

Exercise 29.11

Exercise 29.1

1

Show that does not exist.

2

Find k so that may exist, where .

3

Show that does not exist.

4

Let f(x) be a function defined by .

Show that does not exist.

5

Let . Prove that does not exist.

6

Let . Prove that does not exist.

7

Find , where

8

If . Find and .

9

Find , if .

10

Evaluate , where

11

Let a₁, a₂, …….a_n be fixed real numbers such that f(x) = (x – a₁) (x – a₂) …….(x – a_n)

What is ? For a ≠ a₁, a₂, …..,a_n compute

12

Find

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

13

Evaluate the following one - sided limits:

(xi)

14

Show that does not exist.

15

Find:

15

Find:

15

Find:

16

Prove that for all a ∈ R. Also, prove that .

17

Show that .

18

Find . Is it equal to .

19

Find .

20

Evaluate (if it exists), where .

21

Show that does not exist.

22

Let and if , find the value of k.

Exercise 29.2

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

Exercise 29.3

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

20

Evaluate the following limits:

21

Evaluate the following limits:

22

Evaluate the following limits:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate the following limits:

26

Evaluate the following limits:

27

Evaluate the following limits:

28

Evaluate the following limits:

29

Evaluate the following limits:

30

Evaluate the following limits:

31

Evaluate the following limits:

32

Evaluate the following limits:

33

Evaluate the following limits:

34

Evaluate the following limits:

Exercise 29.4

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

20

Evaluate the following limits:

21

Evaluate the following limits:

22

Evaluate the following limits:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate the following limits:

26

Evaluate the following limits:

27

Evaluate the following limits:

28

Evaluate the following limits:

29

Evaluate the following limits:

30

Evaluate the following limits:

31

Evaluate the following limits:

32

Evaluate the following limits:

33

Evaluate the following limits:

34

Evaluate the following limits:

Exercise 29.5

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

If , find the value of n.

13

if , find all possible values of a.

14

If , find all possible values of a.

15

If , find all possible values of a.

16

If , find all possible values of a.

Exercise 29.6

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

20

Evaluate the following limits:

, where a is a non-zero real number.

21

Evaluate the following limits:

and , then prove that f(-2) = f(2) = 1.

22

Show that

To Prove:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate:

26

Evaluate:

Exercise 29.7

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

20

Evaluate the following limits:

21

Evaluate the following limits:

22

Evaluate the following limits:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate the following limits:

26

Evaluate the following limits:

27

Evaluate the following limits:

28

Evaluate the following limits:

29

Evaluate the following limits:

30

Evaluate the following limits:

31

Evaluate the following limits:

32

Evaluate the following limits:

33

Evaluate the following limits:

34

Evaluate the following limits:

35

Evaluate the following limits:

36

Evaluate the following limits:

37

Evaluate the following limits:

38

Evaluate the following limits:

39

Evaluate the following limits:

40

Evaluate the following limits:

41

Evaluate the following limits:

42

Evaluate the following limits:

43

Evaluate the following limits:

44

Evaluate the following limits:

45

Evaluate the following limits:

46

Evaluate the following limits:

47

Evaluate the following limits:

48

Evaluate the following limits:

49

Evaluate the following limits:

50

Evaluate the following limits:

51

Evaluate the following limits:

52

Evaluate the following limits:

53

Evaluate the following limits:

54

Evaluate the following limits:

55

Evaluate the following limits:

56

Evaluate the following limits:

57

Evaluate the following limits:

58

Evaluate the following limits:

59

Evaluate the following limits:

60

Evaluate the following limits:

61

Evaluate the following limits:

62

Evaluate the following limits:

63

Evaluate the following limits:

If

Exercise 29.8

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

, where f(x) = sin 2x

20

Evaluate the following limits:

21

Evaluate the following limits:

22

Evaluate the following limits:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate the following limits:

26

Evaluate the following limits:

27

Evaluate the following limits:

28

Evaluate the following limits:

29

Evaluate the following limits:

30

Evaluate the following limits:

31

Evaluate the following limits:

32

Evaluate the following limits:

33

Evaluate the following limits:

34

Evaluate the following limits:

35

Evaluate the following limits:

36

Evaluate the following limits:

37

Evaluate the following limits:

38

Evaluate the following limits:

Exercise 29.9

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

Exercise 29.10

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits:

11

Evaluate the following limits:

12

Evaluate the following limits:

13

Evaluate the following limits:

14

Evaluate the following limits:

15

Evaluate the following limits:

16

Evaluate the following limits:

17

Evaluate the following limits:

18

Evaluate the following limits:

19

Evaluate the following limits:

20

Evaluate the following limits:

21

Evaluate the following limits:

22

Evaluate the following limits:

23

Evaluate the following limits:

24

Evaluate the following limits:

25

Evaluate the following limits:

26

Evaluate the following limits:

27

Evaluate the following limits:

28

Evaluate the following limits:

29

Evaluate the following limits:

30

Evaluate the following limits:

31

Evaluate the following limits:

32

Evaluate the following limits:

33

Evaluate the following limits:

34

Evaluate the following limits:

35

Evaluate the following limits:

36

Evaluate the following limits:

37

Evaluate the following limits:

38

Evaluate the following limits:

39

Evaluate the following limits:

40

Evaluate the following limits:

41

Evaluate the following limits:

42

Evaluate the following limits:

43

Evaluate the following limits:

Exercise 29.11

1

Evaluate the following limits:

2

Evaluate the following limits:

3

Evaluate the following limits:

4

Evaluate the following limits:

5

Evaluate the following limits:

6

Evaluate the following limits:

7

Evaluate the following limits:

8

Evaluate the following limits:

9

Evaluate the following limits:

10

Evaluate the following limits: