- #1

brycenrg

- 95

- 2

## Homework Statement

Find the limit

lim (sin(3x))/x

x-->0

## Homework Equations

There is two steps which I don't understand how they work, or why they work. Ill show you.

I'm using my answer book to help me out, but it doesn't give a satisfactory explanation.

## The Attempt at a Solution

lim (sin(3x))/x

x-->0

= lim 3(sin(3x))/3x

x-->0

= 3lim (sin(3x))/3x as x -> 0 3x -> 0 Why do I do this maneuver? I understand its for

x-->0 substitution

= 3lim (sin(3x))/3x let theta = 3x

= 3lim (sin(theta))/theta

= 3(1) Why does lim (sin(theta))/theta equal 1?