Question

If limit(x=0), then sin x/x=?

Answer 1

1

Answer 2

if \(x\rightarrow 0 ,then , \frac{\sin x}{x}=1 \)
because \(\lim \limits_{x \rightarrow0}\frac{\sin x}{x}=1\)

Answer 3

haha student outrules his teacher xD

Answer 4

i am not in any kind of race :P

Answer 5

hmm..@Koikkara got it?

Answer 6

hey guys, thanks n specially appreciate u, two...for the tip...!!

Answer 7

well..
sin x/x = sin1 //isnt it? ;)

Answer 8

Something new.........
Just use hopital's rule for that ...
sin(x) / x == cos(x) /1 and cos(x) for x->0 = 1

Answer 9

@Koikkara: It'd be fun to know how you prove \(\dfrac{d}{dx}\sin(x) = \cos(x)\)

Answer 10

taylor series hmm ?

Answer 11

limit definitaion would do it....

Answer 12

infact, taylor series itself makes use of the face that sin'x = cosx :P

Answer 13

Also\[\dfrac{\sin(x)}{x} \ne \dfrac{\cos(x)}{1}\]@Koikkara :P

Answer 14

@shubhamsrg Haha yes, the expansions would work =)

Answer 15

According to L'Hopital's rule, it is circular reasoning for this limit. L'Hopital's rule depends on the knowing that the derivative of sin(x) is cos(x), and in order to have that, we need to know that lim_{x->0} sin(x)/x = 1.

Answer 16

You can use FPM.

Answer 17

Prove the L'Hopital's Rule.

Answer 18

i wont say use of expansions would be good..
since expansion itself uses the fact that sinx ' = cos x

Answer 19

as @hartnn said,,definiton of limits will help our cause..

Answer 20

Maybe term-by-term derivative? @shubhamsrg

Answer 21

use limit definition to prove that derivative....

Answer 22

Oh yes.

Answer 23

\[\frac{\sin(x +h) -\sin(x)}{h}\]Hmm. \(\sin(a + b)\) formula and stuff

Answer 24

or sin C-sin D

Answer 25

leme try geometrically //hmmm



sin x = a/c
we need to find rate of change of sinx if x changes
hmm..