Squeeze theorem question

appplejack

1. The problem statement, all variables and given/known data
Find lim sin4x/3x
x -> 0

2. Relevant equations

3. 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 text book says so.

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Dick

Homework Helper
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.

Last edited:

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

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

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