Limit of sin4x/3x as x approaches 0: Squeeze Theorem

[appplejack]

Homework Statement

Find lim sin4x/3x
x -> 0

Homework Equations

The Attempt at a Solution

I did some algebraic massaging and got

sin4/3x = 4/4 * sin4x/3x = 4/3 * sin4x/4x
but I don't understand how sin4x/4x becomes 1 like my textbook says so.

 

[Dick]

sin(4x)/(4x) isn't 1. The limit as x->0 of sin(4x)/(4x) is 1. Have you proved limit u->0 of sin(u)/u=1? Then just put 4x=u.

 

[appplejack]

sin(4x)/(4x) isn't 1. The limit as x->0 of sin(4x)/(4x) is 1. Have you proved limit u->0 of sin(u)/u=1? Then just put 4x=u.

Yeah you're right.So, It's true that limit u->0 of sin(u)/u=1?

 

[Dick]

Didn't you prove limit u->0 sin(u)/u=1. I doubt they would have given you this problem if they hadn't.