Question

I can't seem to get started here find the limit: as x approaches 0 sin3x/x any help would be appreciated

Answer 1

You need to rely on one of your important limit things: \[\Large\rm \lim_{x\to0}\dfrac{\sin x}{x}=1\]

Answer 2

So if we have:\[\Large\rm \lim_{x\to0}\frac{\sin(\color{orangered}{3x})}{x}\]We can't get the 3 outside of the sine, that's what's causing a problem for us.
So we want to form a 3 in the bottom of this fraction so it matches the angle inside of our sine function.

Answer 3

We'll multiply the top and bottom by 3, and write it like this:\[\Large\rm \lim_{x\to0}\frac{\sin(\color{orangered}{3x})}{x}\cdot \frac{3}{3}\qquad=\qquad 3\lim_{x\to0}\frac{\sin(\color{orangered}{3x})}{\color{orangered}{3x}}\]

Answer 4

Understand how to apply the identity from there?

Answer 5

yeah sorry my calculus is rusty, was helping a friend and didn't quite understand how to do this been 2 years since calc 1 :( thanks a lot! :D

Answer 6

cool c: