## DLS 2 years ago Someone tell about signum and GIF ?

1. shubhamsrg

You must have atleast seen there graphs? Tell me what you do not understand in this ?

2. DLS

explain GIF with example.. maybe with the help of this example

3. shubhamsrg

The largest integer less than, or equal to , a given real number <- this is GIF

4. shubhamsrg

[7.6] = 7

5. shubhamsrg

[-1.2] = -2

6. shubhamsrg

[3] = 3

7. DLS

$LARGE lim_{x rightarrow 2} {[2-x]+[x-2]-x}$

8. DLS

math processing error |:

9. shubhamsrg

10. DLS

holdon

11. DLS

$\LARGE \lim_{x \rightarrow 2} {[2-x]+[x-2]-x}$

12. DLS

3 -3 N/T 0

13. shubhamsrg

Here,there are 2 ways, 1) you'll have to check right hand and left hand limits separately 2) make use of the fact that [x] + [-x] = -1

14. shubhamsrg

Using 2nd one quickly guides you towards the answer. 1st method also isnt lengthy enough, try it.

15. DLS

is it -3?

16. shubhamsrg

Oh wait, 2nd method fails here, its limit.

17. shubhamsrg

18. DLS

hmm

19. shubhamsrg

for x->2- , we have -3 for x->2+ , we have again -3 but when x=2 , we have -2.

20. shubhamsrg

the 2nd fact is only valid if x is not an integer, which is not the case here.

21. DLS

22. shubhamsrg

Oh, :O kya answer hai ?

23. DLS

-3

24. shubhamsrg

2 pe to fail ho jata hai, mai nahi manta.

25. DLS

:/..

26. DLS

wo [ ] GIF hai

27. shubhamsrg

Ha bhai, GIF hai.

28. DLS

$\LARGE \lim_{h \rightarrow 0} {[2-(2+h)]+[(2+h)-2]-(2+h)}$

29. DLS

$\LARGE {[-h]+[h]-2-h}$

30. DLS

-1+0-2-h=-3

31. DLS

this is what book says idk now >.<

32. DLS

i got it btw

33. DLS

but why [-h] ke liye -1 ? and [h] ke liye 0..ye bata bus

34. shubhamsrg

[-h] ke ;iye -1 aur [h] ke liye 0 nahi hai,1 baar h- liya to 0 aur -1 aya, 1 baar h+1 liya to -1 aur 0 aya isme bhi h=0 pe -2 ayega, mai to ab bhi kahunga DNE

35. DLS

..:/

36. shubhamsrg

hmm, purane ques dekh raha hu main, exact value pe check nahi kiya hua hai. WO shayd sirf continuity me karte hain.

37. shubhamsrg

To sahi hai fir, -3 hoga, mere method se , ya fir book ke method se. kyunki exact value pe nahi check kar rahe to fir 2nd method laga sake hai, -3 aa jayega.

38. shubhamsrg

Samjh aya? continuity me exact value pe bi check karenge, limit me nahi

39. DLS

abhi cont. nahi pada,padu kya? :/ abhi sunne me confusing lag rha hai

40. shubhamsrg

Continuity kuch nahi hai bas limits ka application hai. Time aane pe padh liye, abhi rehn de. Abhi ke liye samjh aya?

41. DLS

kinda

42. DLS

not this but but why [-h] ke liye -1 ? and [h] ke liye 0..ye bata bus

43. shubhamsrg

jab h->0- hai, tab [h] kya hoga batao ?

44. DLS

wahi to nahi pata :|

45. DLS

kya kyu kaise

46. shubhamsrg

0 se chota hai, samjh lo -0.999999.. hai, iska Greatest integer, -1 hoga right ?

47. shubhamsrg

-0.9999 nahi, -0.00000.....1 hai

48. DLS

fir to 0 hoga greatest..?

49. DLS

|dw:1358615551512:dw|

50. DLS

|dw:1358615642858:dw|

51. DLS

when u come back explain with this diagram

52. shubhamsrg

|dw:1358616738133:dw|

53. shubhamsrg

|dw:1358616759494:dw| Getting it ?

54. DLS

-1>0 ?

55. shubhamsrg

o.O

56. DLS

-0.00000001 hai to 0 hoga next greaatest why -1

57. shubhamsrg

wo greatest number jo -0.0000001 se chota ho !

58. DLS

chod lol/ confusing

59. shubhamsrg

kya baat kar rahe ho yaar! -1 bada hai ya -0.000001 ?

60. DLS

61. shubhamsrg

0

62. DLS

to?

63. shubhamsrg

number line me right side wala nio. hi bada hoga na.

64. shubhamsrg

bhaijo no. result me ayega wo -0.00001 se chota hona chaiye, 0 usse bada hota hai.

65. DLS

oo

66. shubhamsrg

??