## jatinbansalhot Group Title find out the limit of the following ( sin x ) / x where x -> 0 2 years ago 2 years ago

1. ankit709 Group Title

=1

2. jatinbansalhot Group Title

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

3. furan143 Group Title

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

4. furan143 Group Title

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

5. jatinbansalhot Group Title

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

6. ankit709 Group Title

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

7. jatinbansalhot Group Title

i will get 0

8. furan143 Group Title

offcourse buddy

9. ankit709 Group Title

u can apply dy/dx

10. furan143 Group Title

actually 0/0 is a indeterminate value

11. jatinbansalhot Group Title

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

12. ankit709 Group Title

this is L hospital rule

13. jatinbansalhot Group Title

furan.. yah that would be indeterminate state

14. jatinbansalhot Group Title

ohhh.. hospital ....

15. furan143 Group Title

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

16. furan143 Group Title

buddy L'hospital rule is not the actual prrof

17. furan143 Group Title

srry proof

18. ankit709 Group Title

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

19. jatinbansalhot Group Title

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 Group Title

really too long ? i thought it would be very simple

21. furan143 Group Title

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

22. jatinbansalhot Group Title

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

23. furan143 Group Title

actually sandwich theorem is like the foundation of calculus

24. furan143 Group Title

proof is not that long but concept is difficult

25. jatinbansalhot Group Title

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

26. furan143 Group Title

I remembers the last step

27. jatinbansalhot Group Title

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

28. CeW Group Title

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

29. furan143 Group Title

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 Group Title

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

31. furan143 Group Title

you are right cew

32. jatinbansalhot Group Title

santosh r u there?

33. experimentX Group Title

yeah

34. jatinbansalhot Group Title

hi experimentX, how are you brooo...

35. experimentX Group Title

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

36. jatinbansalhot Group Title

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

37. jatinbansalhot Group Title

open these three :)

38. experimentX Group Title

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 Group Title

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

40. jatinbansalhot Group Title

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

41. experimentX Group Title

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

42. jatinbansalhot Group Title

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

43. experimentX Group Title

how is epsilon defined??

44. jatinbansalhot Group Title

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

45. experimentX Group Title

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

46. jatinbansalhot Group Title

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 Group Title

thanks experimentX..... :) :)

48. jatinbansalhot Group Title

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

49. experimentX Group Title

sure ...