Find Lim( (sin3x/x) -1) as x -- 0

Question

Find  Lim( (sin3x/x) -1) as x --> 0

zepdrix · Answer

Hey, welcome to OpenStudy! :)

This is our problem?
$$\large\rm \lim_{x\to0}~\frac{\sin(3x)}{x}-1$$

shepherdll · Answer

Yea that is the problem! My answer was 2 but it was wrong so i dont know what to do.

zepdrix · Answer

This is a special limit identity that you learn early on in Calculus,$$\large\rm \lim_{y\to0}\frac{\sin(\color{orangered}{y})}{\color{orangered}{y}}\quad=\quad 1$$The important thing for this identity is that the angle matches the denominator.

zepdrix · Answer

So for your problem,
you need to find a fancy way to get a 3 in the denominator.

You want to create a 3x in the denominator so it matches the argument of the sine.

zepdrix · Answer

Wait... you ended up with 2?
That shouldn't be wrong D: Hmm

zepdrix · Answer

Just for confirmation: https://www.wolframalpha.com/input/?i=limit+as+x+approaches+0+of+(sin(3x))%2Fx-1

shepherdll · Answer

Yea thats what i was thinking. My professor probably made a mistake than.

zepdrix · Answer

Ya, weird :)