FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams. We connect Students who have an understanding of course material with Students who need help. Benefits:- # Students can catch up on notes they missed because of an absence. # Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand # Students can earn better grades, save time and study effectively Our Vision & Mission – Simplifying Students Life Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.” Like Us - https://www.facebook.com/FellowBuddycom

1. Limits and Continuity – Intutive Approach–
Chapter 8
Paper 4: Quantitative Aptitude- Mathematices
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths)

2. Limits
• Fundamental Knowledge
• Its application
2

3. Concept of Limit
x tends to zero or x → 0
x tends to a finite quantity or x → b
x tends to a infinity or x → ∞
3

4. Meaning of x tends to zero
Suppose that the maid of Neeta has to pay a debt of Rs.
104 to Neeta. She pays 50% of a debt every month, when
she will be able to repay the whole amount of debt.
Solution:
Let x be the debt at the end of the any month.
At the end of 1st month, x = Rs. 52
At the end of 2nd month, x = Rs. 26
At the end of 3rd month, x = Rs. 13
4

5. Meaning of x tends to zero – Continued
5

6. Difference between x = 0 & x→0
• If there is a pear and we have to divide it among 100
children then each child gets his share say x, which is
infinitesimally small i.e. x→0.
• On the other hand if there is no pear, then no child will get
any thing i.e. x=0.
6

7. Ram is interesting in getting printed a special type of
visiting cards for promotion of his business. The cost of
composing the visiting card is Rs. 100 (for any number of
visiting cards).
The cost of paper and printing per visiting cards is Rs. 3.
Find the number of visiting cards to be printed in order to
minimize the cost of the visiting card.
Solution:
Let x be the cost per visiting card, then the cost of 10
visiting cards is
= 30 + 100 = 130
7

8. 8

9. Meaning of x→∞
9

10. Intuitive Approach to Limit
10

11. Intuitive Approach to Limit - Continued
If x = 3.01 then f(3.01) = 6.01
If x = 3.001 then f(3.001) = 6.001
II. When x takes the values slightly less than 3
If x = 2.9 then f(2.9) = 5.9
If x = 2.99 then f(2.99) = 5.99
If x = 2.999 then f(2.999) = 5.999
11

12. 12

13. Right Hand Limit
13

14. Left Hand Limit
14

15. Useful theorems on Limits
15

16. Useful theorems on Limits- Continued
16

17. Some important Limits
17

18. Some important Limits- Continued
18

19. Some important Limits- Continued
19

20. Some important Limits- Continued
20

21. L’ Hospital Rule
21

22. Illustrations
22

23. Illustration - 8
23

24. Illustration – 8 – Continued
24

25. Illustration 9
25

26. Illustration 9 – Continued
26

27. Illustration - 10
27

28. Illustration - 11
28

29. Illustration - 12
29

30. Illustration – 12 - Continued
30

31. Illustration - 13
31

32. Illustration – 13 - Continued
32

33. Illustration - 14
33

34. Illustration – 14 - Continued
34

35. Illustration - 15
35

36. Illustration – 15 – Continued
36

37. Illustration - 16
37

38. Illustration – 16 - Continued
38

39. Illustration - 17
39

40. Illustration – 17 - Continued
40

41. Illustration - 18
41

42. Illustration – 18- Continued
42

43. Illustration – 18- Continued
43

44. Illustration - 19
44

45. Illustration – 19 – Continued
45

46. Illustration 20
46

47. Illustration 21
47

48. Illustration 21 – Continued
48

49. Illustration 22
49

50. Illustration 22 – Continued
50

51. Illustration 23
51

52. Illustration 23 – Continued
52

53. Thank you
53