## jatinbansalhot 3 years ago find out the limit of the following ( sin x ) / x where x -> 0

1. ankit709

=1

2. jatinbansalhot

plz explain too . i found out it to be 0. u r right it is 1 how

3. furan143

answer is 1,actually it's proof is a bit theoretical .if you want any proof please refer some standard text

4. furan143

it's proof is well known and is known as sandwich theorem

5. jatinbansalhot

as x reduces, the sin of x also reduces, then why 1

6. ankit709

if u put the value of limit then u will get 0/0 form

7. jatinbansalhot

i will get 0

8. furan143

offcourse buddy

9. ankit709

u can apply dy/dx

10. furan143

actually 0/0 is a indeterminate value

11. jatinbansalhot

derivative ? but i don't know the derivative i'm beginner but soon be older :D :D hahahaa

12. ankit709

this is L hospital rule

13. jatinbansalhot

furan.. yah that would be indeterminate state

14. jatinbansalhot

ohhh.. hospital ....

15. furan143

I think the proof starts from some sort of triangle & using some inequality conditions

16. furan143

buddy L'hospital rule is not the actual prrof

17. furan143

srry proof

18. ankit709

I KNOW but u also know that proof of this equation is 2 long

19. jatinbansalhot

i think for the time being, it is enough that the limit of that is = 1 .... as i will advance in this calculus, i will come across the proof soon and become familiar with that ...

20. jatinbansalhot

really too long ? i thought it would be very simple

21. furan143

okay then you better use L'hospital's rule then

22. jatinbansalhot

yah.... i will ... :) thanks all frnds in here .. :) :) :) :) :) :) :) :) :) :) :) :) :) :) :)

23. furan143

actually sandwich theorem is like the foundation of calculus

24. furan143

proof is not that long but concept is difficult

25. jatinbansalhot

sandwich.... i need to work up at great deal :) :) i will .. bcoz i want to be so perfect in calculus :)

26. furan143

I remembers the last step

27. jatinbansalhot

it's alright no problem. thanks you all alot...... really helpful for me.... :)

28. CeW

sin(x) for small x is x. x/x is 1 for any x.

29. furan143

cosx<(sinx/x)<1 here (sinx/x) is sandwiched between cosx & 1 (here not that cosx is also 1 when x tends to zero so sinx/x has no other option other than to tend to zero) that's why it has got the name sandwich or squeeze theorem

30. CeW

sin(x) / x does not approach 0 in the limit of x -> 0 !!

31. furan143

you are right cew

32. jatinbansalhot

santosh r u there?

33. experimentX

yeah

34. jatinbansalhot

hi experimentX, how are you brooo...

35. experimentX

doing fine ... i might be offline pretty soon .. |dw:1334192708048:dw|

36. jatinbansalhot

before being, could you expect to have some time with me or not ?

37. jatinbansalhot

open these three :)

38. experimentX

you see arc there = it's value = $$r\theta$$, when $$\theta->0$$, the ARC and H seem to be one line. or h/rQ -> tends to one as Q->0 h/r = sinQ => sinQ/Q->1 as Q->0

39. jatinbansalhot

i want to know why epsilon is smaller than a - x0 and x1 - a

40. jatinbansalhot

yah.... both approach toward 0 i saw that

41. experimentX

It's not both approach to zero ... it's how their ratio approach as Q approaches to zero -> that is limit.

42. jatinbansalhot

why epsilon is smaller than a - x0 and x1 - a ............................... :)

43. experimentX

how is epsilon defined??

44. jatinbansalhot

i know how epsilon is defined but why epsilon is smaller than a - x0 and x1 - a ............................... :)

45. experimentX

i don't know how epsilon is defined ... is it |x-a| < epsilon or |f(x) - L | < epsilon

46. jatinbansalhot

omggggggggggggg... how i can get answer to my question... here no one knows about limit definition properly..... ... leave it i try to google it... :D

47. jatinbansalhot

thanks experimentX..... :) :)

48. jatinbansalhot

ExperimentX... I go and study mathematics more and more if again any ques i would come back :) take care brooo :)

49. experimentX

sure ...