how to solve this formula limits's formula

Question

I have already known one way to solve this formula but I just want to know the easier way to do so: $$\lim_{ u \to 0} \frac{\sin(u)}{u}=1$$

Please kindly help me!! Thank You.

See also: https://proofwiki.org/wiki/Limit_of_Sine_of_X_over_X — lab bhattacharjee, Jul 05 '15 at 15:43

score 0 · Answer 1 · edited Jul 05 '15 at 16:29

0

Using L'hopital's rule,

$$\lim_{u \to 0}\frac{\sin u}{u} = \lim_{u \to 0} \frac{\frac{d}{du}\sin u}{\frac{d}{du}u} = \lim_{u \to 0} \cos u = 1$$

edited Jul 05 '15 at 16:29

wythagoras

answered Jul 05 '15 at 15:48

John_dydx

Sir my country doesn't study this equation in high school so I don't know what it is – Mang Sopheak Jul 05 '15 at 15:53
Can u pls solve another way ? What is l'hospital's – Mang Sopheak Jul 05 '15 at 15:54
3

@John, this proof is circular. Have a look [here](http://meta.math.stackexchange.com/questions/13008/why-are-people-so-interested-in-finding-limits-without-lh%C3%B4pitals-rule/13011#13011). – k170 Jul 05 '15 at 15:55
@k170, thanks. Very interesting post! – John_dydx Jul 05 '15 at 16:00
@MangSopheak, please see the other previous posts of this question as this question is a duplicate. – John_dydx Jul 05 '15 at 16:04

1 Answers1