Question

lim of x as sin(3x)/(2x) approaches 0

Answer 1

try graphing it.

Answer 2

do you know how to evaluate
\[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}?\]

Answer 3

This limit should have been already introduced to you by the squeeze theorem (or at least this is the first way I learned what the above limit is)

\[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1\]
commit this limit to memory
it will be useful


let's take this limit and see if i can give you a hint on how to do your problem

since there is a 3x inside that sin
let's let u equal 3x

and if u goes to 0 then 3x goes to 0 since u=3x
and since 3 doesn't go to 0 then the x must go to 0


so anyways
\[\lim_{x \rightarrow 0}\frac{\sin(3x)}{3x}=1 \]
try to use this limit here for your problem

you may find it necessary to multiply by a 1 to do so