Question

find out the limit of the following
( sin x ) / x where x -> 0

Answer 1

=1

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

i will get 0

Answer 8

offcourse buddy

Answer 9

u can apply dy/dx

Answer 10

actually 0/0 is a indeterminate value

Answer 11

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

Answer 12

this is L hospital rule

Answer 13

furan.. yah that would be indeterminate state

Answer 14

ohhh.. hospital ....

Answer 15

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

Answer 16

buddy L'hospital rule is not the actual prrof

Answer 17

srry proof

Answer 18

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

Answer 19

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 ...

Answer 20

really too long ? i thought it would be very simple

Answer 21

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

Answer 22

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

Answer 23

actually sandwich theorem is like the foundation of calculus

Answer 24

proof is not that long but concept is difficult

Answer 25

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

Answer 26

I remembers the last step

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

you are right cew

Answer 32

santosh r u there?

Answer 33

yeah

Answer 34

hi experimentX, how are you brooo...

Answer 35

doing fine ... i might be offline pretty soon ..