- #1

- 2

- 0

## Homework Statement

lim x-> 0 ( sin(5x) - 3x ) / ( 3x )

## Homework Equations

(a - b) / c = (a / c) - b

## The Attempt at a Solution

(1/3) lim x->0 ( sin(5x) / x ) - 3x

= (1/3) lim x->0 ( sin(5x) / x )( 5 / 5) - 3x

= (5/3) lim x->0 ( sin(5x) / 5x ) - 3x

= (5/3) * 1 - 3x

= (5/3) - 3x

= (5/3)

I use WolframAlpha to check whether or not my answers are correct. WolframAlpha and I are having a disagreement (even though I am most likely wrong) about this problem. I say 5/3, it says 2/3. Can someone please explain where I went wrong?

Sorry, I tried using LaTeX but I just got annoyed.